Indexing for Moving Objects in Multi-Floor Indoor Spaces That Supports Complex Semantic Queries

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1 International Journal Geo-Information Article Indexg for Movg Objects Multi-Floor Indoor Spaces That Supports Complex Semantic Queries Hui L 1,2, *, Lg Peng 1,2, *, Si Chen 3, Tianyue Liu 4 Tianhe Chi 1,2 1 Institute Remote Sensg Digital Earth, Chese Academy Sciences, CAS Olympic S & T Park, No. 20 Datun Road, P.O. Box 9718, Beijg , Cha; chith@126.com 2 University Chese Academy Sciences, No. 19A Yuquan Road, Beijg , Cha 3 Department Computer Science, University Massachusetts Boston, Boston, MA 02125, USA; sichen219@gmail.com 4 Beijg Jghang Computation Communication Research Institute, Beijg , Cha; liuty@radi.ac.cn * Correspondence: lhui@whu.edu.cn (H.L.); penglgradi@126.com (L.P.); Tel.: (H.L.) Academic Editors: Sisi Zlatanova, Kourosh Khoshelham, George Sithole Wolfgang Kaz Received: 17 May 2016; Accepted: 18 September 2016; Published: 27 September 2016 Abstract: With emergence various types door positiong technologies (e.g., radio-frequency identification, Wi-Fi, ibeacon), how to rapidly retrieve door cells movg s has become a key factor that limits those door applications. Euclidean distance-based dexg techniques for outdoor movg s cannot be used door spaces due to existence door obstructions (e.g., walls). In addition, currently, dexg door movg s is maly based on space-related query less frequently on query. To address se two issues, present study proposes a multi-floor adjacency cell -based dex (MACSI). By tegratg door cellular space with space, MACSI subdivides open cells (e.g., hallways lobbies) usg space syntax optimizes adjacency distances between three-dimensionally connected cells (e.g., elevators stairs) based on caloric cost that extends sgle floor door space to three dimensional door space. Moreover, based on needs query, this study also proposes a multi-granularity door hierarchy tree establishes trajectories. Extensive simulation real-data experiments show that compared with door trajectories delta tree (ITD-tree) -based dex (SI) MACSI produces more reliable query results with significantly higher query update efficiencies; has superior expansion capability; supports multi-granularity complex queries. Keywords: door adjacency matrix; door complex query; trajectory; dexg for door movg s 1. Introduction Accordg to available statistics, humans spend 87% ir time door spaces [1], such as private residences fice buildgs. Thus, humans produce vast numbers door movg trajectories. For example, on 5 March 2016, 15 operation les Beijg Subway hled a daily passenger volume million [2]. Effectively managg massive data door cells movg s is particularly important for many applications, cludg trackg [3], door navigation [4] emergency evacuation [5]. Due to buildg obstructions, Global Positiong Systems (GPS) cannot obta accurate positiong results door environments. Recently, with development door positiong technology, large volumes trackg data have become available, greatly promotg vigorous development ISPRS Int. J. Geo-Inf. 2016, 5, 176; doi: /ijgi

2 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, development door Location Based Service (LBS). Indoor positiong uses short-distance development door Location Based door Service Location (LBS). Based IndoorService positiong (LBS). uses Indoor short-distance positiong positiong uses short-distance positiong technologies, such as Radio Frequency Identification (RFID) [6], WiFi [7,8] technologies, ZigBee positiong such as Radio technologies, Frequency such Identification as Radio (RFID) Frequency [6], WiFi Identification [7,8] (RFID) ZigBee [6], [9]. WiFi The representation [7,8] ZigBee [9]. The representation positiong signals varies between outdoor door positiong. For [9]. The positiong representation signals varies positiong between outdoor signals varies door between positiong. outdoor Fordoor example, positiong. outdoor For example, outdoor positiong signals GPS generally consist latitude longitude positiong example, signals outdoor GPS positiong generally consist signals latitude GPS generally longitude consist coordates, latitude while Symbolic longitude coordates, while Symbolic cells are more frequently used to represent door positiong [10]. cells coordates, are more frequently while Symbolic used to represent cells are more door frequently positiong used [10]. to represent door positiong [10]. In addition, Euclidean distance or road network distance is ten used as outdoor In addition, Euclidean distance or road network distance is ten used as outdoor measurement stard, although former cannot be used door spaces because various measurement stard, although former cannot be used door spaces because various constrats, such as walls. As shown 1, distance between s O1 O2 cannot be constrats, such as walls. As shown measured usg straight-le distance; 1, stead, distance between length s le O1 connectg O2 C3, cannot C2, be C1, C9, measured C6 C5 usg (red le) straight-le should be used distance; for stead, door space. length length Outdoor areas le le connectg connectg conta free C3, C3, space. C2, C2, C1, C1, As C9, C9, shown C6 C6 C5 C5 (red (red 2, le) le) distance should should be between used be used for for movg door door space. space. O1 Outdoor Outdoor O2 areas areas can be conta conta measured free free space. space. usg As As shown shown straightle distance 2, 2, distance distance or road between between network distance movg movg for outdoor O1 O1 space. O2 O2 can can In beaddition, measured measured from usg usg perspective straight-le le distance distance spatial cognition, or road or road network network user distance distance dem for for for door outdoor outdoor positiong space. space. Inaccuracy addition, In addition, [11] fromis from significantly perspective perspective higher spatial than spatial cognition, cognition, that outdoor user spaces, dem user dem for door for door establishment positiong positiong user accuracy accuracy trust [11] [12,13] is significantly [11] is significantly for door spaces higher higher is than also that than more that outdoor outdoor complex. spaces, spaces, establishment establishment user trust user [12,13] trust for[12,13] doorfor spaces door is also spaces moreis complex. also more complex Euclidean Euclidean distance distance real real distance. distance. 1. Euclidean distance real distance. 2. Movg distance an outdoor space. 2. Movg distance an outdoor space. 2. Movg distance an outdoor space. Due to aforementioned differences, outdoor movg management technology, which Due to aforementioned differences, outdoor movg management technology, which is very mature, cannot be applied to door spaces. Currently, research on door movg is very mature, cannot be applied to door spaces. Currently, research on door movg

3 ISPRS Int. J. Geo-Inf. 2016, 5, Due to aforementioned differences, outdoor movg management technology, which is very mature, cannot be applied to door spaces. Currently, research on door movg dices [14 17] has maly focused on perspective spatial space, typically only considerg movg s sgle-floor door spaces. Few studies have considered movg s multi-floor door spaces spaces. Indoor movg databases have extensive door user data. The combation door cellular spaces to provide users with stable efficient searchg capabilities can create numerous busess opportunities. For example, onle-to-fle applications have undergone vigorous development recent years allow creasg numbers users to search for contents that y are terested onle experience services fle. Various types search needs are associated with door scenes. For example, a user can use an app to search for fried squid rgs. The app returns a list relevant restaurants which are sorted based on ir distances, user arrives at selected restaurant with help door navigation system. Similarly, a shoppg mall operator can search for users who ten go to movie ater after shoppg deliver latest movie formation to m. Due to particularity door environments positiong issues, this paper aims to establish an effective dex for door movg s multi-floor door spaces that can support typical 3d spatial queries. By combg cell spaces, multi-granularity cells searches can be realized. A series experiments are used to prove that system has better query, update, expansion performances. In summary, this study makes followg ma contributions: 1. A new dexg strategy for door movg s, i.e., multi-floor adjacency cell -based dex (MACSI), is proposed. This dex not only considers adjacency relation between simple door cells (e.g., room) but also contas open cells (e.g., hallways lobbies) cells connected across floors (e.g., elevators stairs). Open cells are subdivided usg space syntax to ensure that adjacency cellular spaces are reasonable, adjacency distances between cells connected across floors are optimized based on caloric cost. To authors knowledge, this is first time that an dex for door movg s, based on an adjacency relation between door cells, has been exped from sgle-floor to multi-floor door spaces. 2. The present study proposes an door multi-granularity hierarchy tree (MGSH-tree) that supports queries for complex door cells s has improved expansion capability. 3. A trajectory model based on door MGSH-tree is proposed. This model supports queries for complex trajectories addresses a shortcomg traditional trajectories, which only represent user behavior pots. This model provides a more diverse trajectory search service for applications assists numerous applications to achieve efficient trajectory retrieval analysis. 4. Indoor trajectories delta tree (ITD-tree) [14] performance is relatively good for door movg s based on adjacency relation between door cells, -based dex (SI) [18] is currently one only a few dices for door spaces. To demonstrate superiority MACSI door cell spaces spaces, experiments are performed on simulated real data sets. The MACSI is found to be advantageous over ITD-tree SI queries for cells, s trajectories, MACSI is more applicable to actual door application scenarios. The rest this paper is organized as follows: Section 2 summarizes previous studies related to present study elucidates ir differences; Section 3 defes some basic concepts; Section 4 describes MACSI detail; Section 5 demonstrates advantages MACSI through a series comparative experiments. Section 6 provides conclusion this study an outlook for future work.

4 ISPRS Int. J. Geo-Inf. 2016, 5, Related Work 2.1. Indexg Outdoor Movg Objects Currently, several Euclidean distance-based dexg techniques exist for movg s, such as R-tree variant-based temporal partitiong R(TPR)-tree [19] time-parameterized R* (TPR*)-tree [20], which can be used to dex current future positions movg s, as well as multi-version 3-dimensional R(MV3R)-tree [21], historical R(HR)-tree [22] trajectory-bundle(tb)-tree [23], which can be used to dex historical trajectories movg s. Fally, fixed network R(FNR)-tree [24], movg s networks (MON)-tree [25] dynamic sketched-trajectory R(DSTR)-tree [26] dex movg s based on road networks Representation Space Subdivision Indoor Spaces Indoor movg s are subject to door space constrats; refore, representation modelg door spaces, space subdivision plays a particularly important role management door movg s [27 29]. To summarize, methods for subdividg door space are geometric method, graph method, a combation se. The geometric method attends to expression an door space [30], which maly cludes a raster model [31 34] a vector model based on boundary [30,35,36]. The raster model is composed regular [31] irregular grids [32 34]. The graph method is a popular method modelg door spaces. Jensen et al. [37] established an door connectivity graph model with door rooms as nodes doors as edges. In addition, Yang et al. [38], Yuan et al. [39], Kang et al. [40] established models based on graphs. The combation method uses advantages each method to support multi-purpose management. Becker et al. [41] proposed a multi-layered space-event model that extends node-relation-structure (NRS) to multiple spatial layers, cludg geometric, topological, sensor layers. Li et al. [42] proposed a model door space that accounts for geometric topological characteristics space can represent its connectivity geometric characteristics. Zlatanova et al. [43,44] proposed a conceptual framework that is concerned with physical conceptual subdivisions door space rooted followg six concepts: Space, Partition, Agent, Activity, Resource Modifier Indexg Indoor Movg Objects The adaptive cell-based dex for door movg s (ACII) proposed by Sh et al. [45] dexes historical current moments. Jensen et al. [15] proposed reader-time R (RTR)-tree time parameter pot R (TP 2 R)-tree. The core idea RTR-tree is to segment an s trajectory to several lear elements. The TP 2 R-tree troduces time parameter to dexg trajectory pots. Alamri et al. [14,16,17] proposed an dex for movg s based on connectivity door cells. This dex supports various types searches (cludg searches for connectivity k-nearest neighbors [k-nn]) but gives less consideration to open cells (e.g., hallways lobbies) three-dimensionally connected cells (e.g., stairs elevators). Alamri et al. s dex is maly used for dexg movg s a sgle-floor door space. Based on Alamri et al. s door adjacency cells, here, open cells (e.g., hallways lobbies) are subdivided usg space syntax [46 48], adjacency distances between three-dimensionally connected cells (e.g., stairs elevators) are optimized based on caloric cost, reby expg application dexg from sgle-floor door spaces to multi-floor door spaces Indoor Semantic Indexg J et al. [49] divided an door space to rooms, doors, sensors stationary s established relations between movg s door elements. Ben et al. [18] proposed an SI that ally classifies door cells supports -based queries. However, because SI performs dexg through limited categories, SI has a limited expansion

5 ISPRS Int. J. Geo-Inf. 2016, 5, capability. In addition, SI provides relatively weak support for spatial constrat-based searches (e.g., searches for k-nn connectivity). The MACSI tegrates door cellular space with spaces improves fe-graed dexg keyword expansion capabilities SI through verted dexg. In summary, contrast to dexg movg s outdoor spaces, characteristics multi-floor searches searches must also be comprehensively considered for door spaces. Therefore, it is vital to establish an dex for movg s multi-floor door spaces that supports complex searches. 3. Prelimary This section provides formal defitions some basic concepts. Section 3.1 defes concepts relatg to door cellular spaces; Section 3.2 defes concepts relatg to door spaces; Section 3.3 provides formal defition door trajectories. Table 1 lists notations used throughout this paper. Table 1. Notations used throughout this paper. Notation C T O CID FID BID EDist(Oi, Oj) CDist(Oi, Oj) RDist(Oi, Oj) STree SRoot SiTr Meang Cellular space Time Movg Cell ID Floor ID Buildg ID The Euclidean distance between Oi Oj The number hops cells between Oi Oj The actual distance between Oi Oj Semantic tree The root tree Semantic trajectory 3.1. Defition Indoor Cellular Spaces Defition 1. For a given set cells, C = {C1, C2, C3,..., Cn}, if any arbitrary, Oi, does not need to pass any or cell when movg from Cx to Cy, where x n, y n, n Cx Cy are adjacency cells. Defition 2. For a given set cells, C = {C1, C2, C3,..., Cn}, for any two arbitrary movg s, Oi(xi, yi) Oj(xj, yj), CDist(Oi, Oj) = Ci, Cj,..., Cn 1 represents number cells that must be passed mus 1. RDist(Oi, Oj) is defed as actual door distance that Oi must travel to reach Oj, Edist is defed as planar distance between Px(xi,yi) Px(xj,yj) (). As shown 1, cellular distance between O1 O2 is C3, C2, C1, C9, C6, C5 1 = 5; length dotted le is Euclidean distance between O1 O2 (EDist(O1, O2)); length red le is actual distance between O1 O2 (RDist(O1, O2)) Defitions Indoor Semantic Meangs Defition 3. For a given set door cell keywords, K = {K1, K2, K3,..., Ki,..., Kn}, for any door cell, Ci, its cellular meang is expressed by SCi = {Ci,{K1, K2,...,Ki,..., Kn}}, where. Defition 4. For a given set movg keywords, J = {J1, J2, J3,..., Jn}, for any arbitrary movg, Ox, its meang is expressed by SOx = {Ox,{J1, J2,... Ji,..., Jn}}, where.

6 ISPRS ISPRS Int. Int. J. J. Geo-Inf. Geo-Inf. 2016, 2016, 5, 5, node contag Ki can be found, n node is expressed by Si = {SRoot, SLevel2, SLevel3,, Defition 5. For a given keyword, Ki, a given root node tree, SRoot, if re is SLeveln} ( depth Si: SDepth = SiTr 1, where SiTr represents number nodes a node access path, SiTr = SRoot- > SLevel2- > SLevel3 - >... - > SLeveln, through which node trajectory). contag Ki can be found, n node is expressed by Si = {SRoot, SLevel2, SLevel3,..., SLeveln} ( depth Si: SDepth = SiTr 1, where SiTr represents number nodes trajectory) Defition Indoor Semantic Trajectories 3.3. Defition Indoor Semantic Trajectories Defition 6. Unlike an outdoor Euclidean space, trajectory a movg an door space Defition cannot 6. Unlike be directly an outdoor expressed Euclidean by space, coordate trajectory series a movg because dog an so door could space lead cannot to be a passg-through--wall directly expressed by coordate phenomenon. series because For dog a given so could set lead s, to a passg-through--wall O = {O1, O2, O3,, phenomenon. On}, a For given a given set set cells, s, C = {C1, O C2, = {O1, C3, O2,, Cn}, O3,..., trajectory On}, a given an door set movg cells, C = {C1, is ten C2, C3, expressed..., Cn}, by, which trajectory is shown an door Table 2, movg where pn represents is ten expressed sequential by, which number is shown trajectory Table 2, positiong where pn represents pot, Cx represents sequential number cellular space trajectory which positiong door movg pot, Cx represents is located, Sti cellular represents space time which at which door door movg movg is located, enters Sti Cx, represents Eti represents time at which time at door which movg door movg enters Cx, leaves Eti represents Cx. Based on time sequential at which relation door between movg Stis, leaves trajectory Cx. Based on user sequential shown relation between 3 can be Stis, expressed trajectory by sequence user shown symbols shown 3 can be expressed 4. by sequence symbols shown 4. Defition Defition 7. For 7. a For given a given trajectory trajectory a certa a certa movg movg,, its its trajectory trajectory is expressed is expressed by, where by, where SDepth(Si) SDepth(Si) = SDepth(STree). = SDepth(STree). Table Table Indoor Indoor positiong positiong log. log. ID Cell Start Time End Time ID Cell Start Time End Time p1 C1 St1 Et1 p1 C1 St1 Et1 p2 p2c2 C2 St2 St2 Et2 Et Et3 Et3 pn pn Cn Cn Stn Stn Etn Etn 3. Record a movg s travel through an door space.

7 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, The sequence a movg trajectory. 4. The sequence a movg trajectory. 4. Index Structure MACSI 4. Index Structure MACSI This section troduces MACSI detail. First, several door queries supported by MACSI This are section described troduces (see Table MACSI 3). Section detail. 4.1 describes First, several overall doordex queries structure supported bymacsi; MACSI are Section described 4.2 troduces (see Table a 3). multi-floor Section 4.1adjacency describescell-based overall tree dex (MAC-tree); structure Section MACSI; 4.3 proposes Sectiona 4.2 troduces multi-granularity a multi-floor adjacency dex (MGSI). cell-based tree (MAC-tree); Section 4.3 proposes a multi-granularity dex (MGSI). Table 3. Queries used experiments conducted present study. Table 3. Queries used experiments conducted present study. Query Type Examples Coarse-graed Query Type s query Fe-graed Coarse-graed s s query query Coarse-graed Fe-graed cells s query query Coarse-graed cells query Fe-graed cells query Fe-graed cells query Complex trajectories query Complex trajectories query 4.1. Overall Index Structure Return all security Examples guards a shoppg mall Return Returnvery all important securityperson guards (VIP) a shoppg customers mall a shoppg mall whose birthdays are today Return very important person (VIP) customers areturn shoppg mall lavatory whosenearest birthdays to are today O1 Return Return restaurant lavatory that nearest sells to fried squid O1 rgs Return restaurant nearest that to sells fried O1 squid rgs Return s that nearest habitually to go O1 to movie ater Return s after shoppg that habitually a shoppg go to movie mall ater after shoppg a shoppg mall 4.1. Overall The MACSI Index Structure considers two dimensions comprehensively: spatial dimensions ( The 5). MACSI For considers spatial dimension, two dimensions this study comprehensively: establishes a MAC-tree spatial by expg Alamri dimensions et al. s ITD-tree. The MAC-tree optimizes open cells three-dimensionally connected cells usg space ( 5). For spatial dimension, this study establishes a MAC-tree by expg Alamri et al. s syntax caloric cost, respectively, hence expg application dexg from sglefloor door spaces to multi-floor door spaces. In addition, MAC-tree dexes movg ITD-tree. The MAC-tree optimizes open cells three-dimensionally connected cells usg space syntax caloric cost, respectively, hence expg application dexg from sgle-floor s a cellular space through a cell- table records historical trajectories door spaces to multi-floor door spaces. In addition, MAC-tree dexes movg s movg s usg an record table. a cellular space through a cell- table records historical trajectories movg s For dimension, present study establishes an MGSI, which cludes usg category an nodes record formed table. usg levels a fe-graed expansion structure generated For via dimension, verted dexg. present As shown study establishes 5, anmovg MGSI, trajectory which cludes O1 is Pizza category Hut- > Guess- nodes> formed KFC- > Nike- usg> Adidas- >7-11. levels The multi-granularity a fe-graed trajectory expansion is obtaed structure generated based on via MGSH-tree. verted To realize dexg. searches Asfor shown movg s, 5, a movg verted trajectory dex for O1 is Pizza movg Hut- s > Guess- is established > KFC- > usg Nike- > Adidas- >7-11. verted Thedexg. multi-granularity A trajectories table is trajectory formed is obtaed by tegratg based on MGSH-tree. record table Towith realize searches trajectories for movg s, is used to a dex verted trajectories dex for movg s. is established usg verted dexg. A trajectories table is formed by tegratg record table with trajectories is used to dex trajectories movg s.

8 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, Overall 5. structure MACSItree. Dark backgrounds dicate dicate -related elements. elements MAC-Tree 4.2. MAC-Tree Generation Cellular Spaces Generation Cellular Spaces The fluence obstructions (e.g., columns, desks chairs) an door environment is ignored. The fluence Based on elements obstructions such as (e.g., walls columns, doors, desks an door space chairs) can be divided an door to environment room cells is ignored. Based on elements such as walls doors, an door space can be divided to room cells open cells (e.g., livg rooms hallways). When a movg moves with a certa cell, next cell that movg passes through must be an adjacent cell. Based on this

9 s, door adjacency distance matrix expansion algorithm [16] can be used to locate correspondg nodes to construct a spatial dex. 7 shows expansion steps usg expansion algorithm based on spatial adjacency relation; terested readers may refer to sultan Alamri s work [14,16,17] for more formation. ISPRS Int. J. Geo-Inf. 2016, 5, Table 4. The adjacency distance table. characteristic C1 adjacency C2 relation between C3 door C4 cells, an adjacency C5 distance matrix C19 door C1 cellular space 0 is obtaed 2 (0 represents 3 a cell, 4 1 represents 2 adjacency cell), 3 thus, by repeatg C2 this process, 2 global 0 distance 1 matrix 2 door2 cellular space can be obtaed. 3 C3 6 shows 3 three-dimensional 1 structures 0 floor 1 1 floor3 2 a certa buildg. Table 4 4 presents C4 adjacency 4 distance2 matrix 1 correspondg 0 cells. When 4 managg door movg 5 s, C5 door 2 adjacency distance 2 matrix 3 expansion 4 algorithm 0 [16] can be used to 3 locate correspondg nodes to construct a spatial dex. 7 shows expansion steps usg expansion algorithm based on spatial adjacency relation; terested readers may refer to sultan C Alamri s work [14,16,17] for more formation. 6. Indoor cellular space. C9 is stairwell, C13 is elevator, C18 is hallway. The top view is is floor 1, 1, bottom view is is floor Table 4. The adjacency distance table. C1 C2 C3 C4 C5... C19 C C C C C C

10 ISPRS Int. J. Geo-Inf. 2016, 5, 176 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, Expansion algorithm. The pots with bold bolditalic italic numbers are expansion pots. 7.7.Expansion algorithm. italic numbers expansion pots. 7. Expansion algorithm.the Thepots pots with with bold numbers areare expansion pots Processg Open Open Cells Processg Open Cells Processg Cells The scale open an open cell isgenerally generally larger than that room cell. open cells (e.g., hallways) Thescale scale an open cell larger than that a room cell. If open hallways) The an cell isis generally larger than that aaroom cell. IfIf open cellscells (e.g.,(e.g., hallways) are are treated as dependent cells, reasonableness reasonableness adjacency distances willwill be damaged. As As are treated as dependent cells, adjacency distances be damaged. treated as dependent cells, reasonableness adjacency distances will be damaged. As shown shown 6, C18 connected hallway. IfIf only walls doors are are usedused to subdivide shown C18 is isa aconnected onlydoors walls doors to subdivide 6, C18 is a6,connected hallway. Ifhallway. only walls are used to subdivide door space, door space, n CDist(C1, C8) = C1,C18,C8 1 = 2 CDist(C1, C5) = C1,C18,C5 = 2. = 2. door space, C8) n= CDist(C1, C8) =1 C1,C18,C8 1 =C5) 2 CDist(C1, C5) C1,C18,C5 n CDist(C1, C1,C18,C8 2 CDist(C1, = C1,C18,C5 2. =However, reality, However, reality, a relatively large= difference exists between CDist(C1, C8)= CDist(C1, C5). reality, a relatively large difference exists between CDist(C1, C8) open-cell CDist(C1, C5). ahowever, relatively large difference exists between CDist(C1, C8) CDist(C1, C5). For problems, For open-cell problems, this study applies space syntax to defe a fer cellular space structure with For open-cell problems, this study applies space syntax to defe a fer cellular space structure with this study applies a smaller scale.space syntax to defe a fer cellular space structure with a smaller scale. a smaller scale. (A,B)Visual Visual le le analysis analysis 8. 8.(A,B) axis axisanalysis. analysis. 8. (A,B) Visual le analysis axis analysis.

11 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, Space syntax volves three ma types analytical methods: axis analysis, visual le analysis convex space analysis. Visual le analysis may cause hallways same direction to be subdivided Space syntax to volves same cell. three As ma shown types analytical 8, methods: only axis needs analysis, to pass visual through le C18 analysis when movg convex from space C1 to analysis. C20 from Visual C1 le to C19. analysis The cellular may cause distance hallways is same same both direction cases, which to be is subdivided clearly unreasonable. to same Convex cell. As space shown analysis defes 8, an doors as only a reference needs topot pass through group C18 a convex when movg space; thus, fromdoors C1 tomay C20 cocide fromwith C1 tonatural C19. The structures cellular distance (e.g., walls is same or doors). both cases, In this which work, is clearly open cells unreasonable. are divided Convex usg space axis analysis. As defes shown doors as a reference 8, hallway pot group spaces aare convex first space; abstracted thus, to doors axes. may Based cocide on ir with perpendicular natural structures relations, (e.g., walls doors are or mapped doors). onto In this hallway work, open axes to cells obta are divided new cross-pots. usg axis Because analysis. Ascurrent shown door positiong 8, hallway accuracy spaces is are typically first abstracted 3 m [50], to axes. nodes Based with on adjacency ir perpendicular distances relations, less than 3 m doors are merged are mapped to a onto new node hallway ( yellow axes tosections obta new cross-pots. 8) to avoid Because excessively current short door distances, positiong which can accuracy result is typically unreasonable 3 m [50], subdivision nodes with adjacency distances cells. Fally, less a perpendicular than 3 m are merged bisector to adjacency a new node nodes (is yellow produced sections to divide m 8) to avoid multiple excessively cells. short distances, which can result unreasonable subdivision adjacency cells. Fally, a perpendicular bisector adjacency nodes is produced to divide m to multiple cells Processg Three-Dimensionally Connected Cells (e.g., Stairs Elevators) Processg Three-Dimensionally Connected Cells (e.g., Stairs Elevators) Considerg dexg movg s a multi-floor door space, Sh et al. [31] separated Considerg floors dexg treated movg three-dimensionally s a multi-floor connected door cells space, (e.g., Sh elevators et al. [31] separated stairs) as regular floors cells. However, treated three-dimensionally this method produces connected unreliable cells query (e.g., results. elevators As shown stairs) as regular stereograph cells. However, 9, this a movg method produces will unreliable select more query distant results. lavatory As shown on same stereograph floor when searchg 9, a for movg a lavatory, whereas will select movg more distant only lavatory needs on to go same upstairs floor to when reach searchg a lavatory for that a lavatory, is closer whereas to him/her. movg only needs to go upstairs to reach a lavatory that is closer to him/her. Bassett Bassett et et al. al. [51,52] [51,52] found found that that walkg walkg speed speed a movg movg its its caloric caloric cost cost varied varied significantly significantly when when a person person ascended ascended descended descended stairs stairs walked. walked. If elevators If elevators stairs stairs are are set set as regular as regular room room cells, cells, reasonableness reasonableness adjacency adjacency distance distance matrix matrix will will be violated. be violated. Here, Here, adjacency adjacency distances distances between between three-dimensionally three-dimensionally connected connected cells cells (e.g., (e.g., stairs stairs elevators) elevators) are are set set based based on on caloric caloric cost, cost, which maly refers to to energy energy consumed by by human activity, different different activity activity tensities tensities have have different different caloric caloric costs. costs. 9. Multi-floor plane. Red regions denote toilets, blue figure is movg. For For stairs, stairs, Chuan Chuan et et al. al. [53,54] [53,54] experimentally experimentally demonstrated demonstrated that that ratio ratio caloric caloric cost cost a a movg movg when when he/she he/she ascends ascends stairs stairs to to that that consumed consumed by by movg movg when when he/she he/she descends descends stairs stairs is is approximately approximately 3:1. 3:1. Therefore, Therefore, this this study, study, adjacency adjacency distances distances are are established established between between three-dimensionally three-dimensionally connected connected cells, cells, symmetric symmetric adjacency adjacency matrix matrix is changed is changed to an to

12 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, an asymmetric adjacency matrix. First, First, stair stair cell cell is islogically divided to two cells, correspondg to ascendg stairs descendg stairs; ascendg-stair cell cell is is segmented to to three three sub-cells. In In adjacency matrix, matrix, ascendg-stair cell has cell an has terval an terval 3, 3, descendg-stair descendg-stair cell has an cell terval has an 1. terval As shown 1. As shown 10, C18 is divided 10, C18 to is an divided ascendg-stair to an ascendg-stair cell a descendg- descendg-stair cell. The ascendg-stair cell. The ascendg-stair cell is divided cell to isthree divided sub-cells. to three Usg sub-cells. distance Usgmeasurement distance cell astair measurement method, global method, matrix global door matrixcellular door space cellular is obtaed space (Table is obtaed 5), showg (Table 5), difference showg difference cost between cost ascendg-stair between ascendg-stair cell descendg-stair cell descendg-stair cell. For example, cell. For CellDist(C1, example, CellDist(C1, C20) = 8, whereas C20) = CellDist(C20, 8, whereas CellDist(C20, C1) = 6. C1) = Multi-floor door cellular space.c18 is stairwell, C19 is elevator. For elevators, fluence streams people special situations (e.g., emergency rescues) For elevators, fluence streams people special situations (e.g., emergency rescues) on on elevators is elimated, problem is simplified to facilitate research on caloric costs. The elevators is elimated, problem is simplified to facilitate research on caloric costs. The costs costs elevator hoistways between different floors are all set to 1. For example, cost from elevator hoistways between different floors are all set to 1. For example, cost from elevator elevator hoistway on floor 1 to elevator hoistway on floor 2 is 1, as is that from elevator hoistway on floor 1 to elevator hoistway on floor 2 is 1, as is that from elevator hoistway on hoistway on floor to elevator hoistway on floor 3. Table 5 presents door adjacency matrix. floor 1 to elevator hoistway on floor 3. Table 5 presents door adjacency matrix. C19 is C19 is elevator hoistway. Clearly, CellDist(C1, C21) = 8 CellDist(C1, C22) = 8, where C21 is a elevator hoistway. Clearly, CellDist(C1, C21) = 8 CellDist(C1, C22) = 8, where C21 is a room cell on room cell on floor 2, C22 is a room cell on floor 3. floor 2, C22 is a room cell on floor 3. Table Table 5. 5.The The adjacency adjacency distance distance table. table. C2 C1 C2... C18 C18 C19 C19 C20 C21 C21 C22 C22 0 C C1 C C2 C C C C C19 C C20 C C C

13 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, MGSI 4.3. MGSI MGSH-Tree MGSH-Tree The MAC-tree reflects spatial topological relation but provides relatively weak support for The meangs. MAC-tree The reflects present spatial study topological establishes relation an MGSH-tree but provides to meet relatively various weak support needs. for meangs. The present study establishes an MGSH-tree to meet various needs. As As shown 11, keywords are first extracted from spatial cells. A shown 11, keywords are first extracted from spatial cells. A hierarchy hierarchy structure is established based on relations between keywords. Considerg structure is established based on relations between keywords. Considerg fegraed needs expansion capability, verted dexg is performed on fe-graed needs expansion capability, verted dexg is performed on leaf nodes MGSH-tree. Relations between keywords door leaf nodes MGSH-tree. Relations between keywords door cells are cells are constructed, significantly improvg query performance ensurg constructed, significantly improvg query performance ensurg expansion expansion capability. capability. For example, For example, hierarchical path hierarchical Pizza Hut path Pizza 11 is Hut Shoppg > Food- 11 is Shoppg- > Pizza- > Food- Pizza > Hut. Pizza- Spaghetti, > Pizza Hut. which Spaghetti, is an verted whichdex is an keyword, verted dex is added keyword, to Pizza is Hut. added to Through Pizza Hut. spaghetti, Through KFC spaghetti, Pizza KFC Hut can Pizza both Hut be found. can both When be Pizza found. Hut When needs Pizza to update Hut needs its to keywords update its(e.g., keywords a new product, (e.g., a new vanilla product, phoenix-tail vanilla prawns, phoenix-tail is added), prawns, a mappg is added), relation abetween mappg relation vanilla between phoenix-tailed vanilla prawns phoenix-tailed Pizza prawns Hut can be Pizza established Hut can be established verted dex. Thus, verted dex. Thus, expansion is achieved. expansion is achieved. 11. Multi-granularity hierarchy tree. 11. Multi-granularity hierarchy tree. 12 shows algorithm by which MACSI queries for nearest cell. The quicksort algorithm 12 showsis maly algorithm used to byobta which nearest MACSI adjacency queries cell for list after nearest rapidly sortg cell. Theadjacency quicksort distances algorithmbetween is maly used search tocell nearest target cell. adjacency cell list after rapidly sortg adjacency distances between search cell target cell Semantic Trajectory Modelg Semantic Trajectory Modelg Outdoor trajectory modelg ten clusters geographic locations stop pots Outdoor users creates trajectorytrajectories modelgbased ten clusters on time geographic sequence after locations formg stop pots users [55]. Because creates an door space trajectories has a relatively based onsmall time scale sequence densely afterdistributed formg features pots [55]. Because outdoor an Euclidean door space distance has a relatively is not suitable smallfor scale an door densely space, distributed outdoor features trajectory modelg outdoor Euclidean methods distance cannot be isused not suitable for door forspaces. an door Usg space, MGSH-tree, outdoor trajectory present study modelg establishes methods a cannot be used for door spaces. Usg MGSH-tree, present study establishes a

14 ISPRS Int. J. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, hierarchy dex for each spatial cell from bottom to top. As a result, trajectory a user hierarchy contas multi-granularity dex hierarchy for each dex spatial for each cellspatial from formation. bottom cell from tobottom top. As to atop. result, As a result, trajectory trajectory a user a user contas multi-granularity contas multi-granularity formation. formation The The algorithm for nearest cell cell search. search. 12. The algorithm for nearest cell search. The trajectories a multi-floor door cellular space are different from those an outdoor Euclidean The trajectories space. In outdoor a multi-floor dexg, door coordate-based cellular space positiong are different pots are from stored, those whereas an outdoor Euclidean itial trajectory space. In pots outdoor obtaed dexg, an coordate-based door cellular space positiong are room pots numbers. are stored, As shown whereas itial trajectory 13, a movg pots obtaed moves from an door Starbucks cellular to space Apple are store room stays numbers. at Apple As store shown for 13, a movg m, subsequently moves reachg from Levis Starbucks store. Then, to Apple movg store goes stays upstairs at to Apple shop. store for The user s m, trajectory subsequently can be reachg simply expressed Levis as store. Starbucks- Then, > Apple- movg > Levis. However, goes upstairs usg only to shop. room numbers br numbers cannot reflect as user s behavior on multiple levels. The user s trajectory can be simply expressed Starbucks- > Apple- > Levis. However, usg only room numbers or br numbers cannot reflect user s behavior on multiple levels. 13. Semantic trajectory. The circle represents movg. As shown 14A, trajectory user 1 is Nike- > Puma- > Adidas, trajectory user 2 is Guess- > Samsung- > Apple, trajectory user 3 is Nike- > Puma- > Adidas. Based on method used to process 13. outdoor Semantic spaces, trajectory. fluence The circle floors represents is elimated, movg. similarity among shapes door planar trajectories is measured. The results show that trajectories user As 1 As shown user 2 are more 14A, 14A, similar. However, trajectory trajectory user user 1 user 1 is 1user is Nike- Nike- 3 are > Puma- both > Puma- terested > Adidas, > Adidas, buyg trajectory sportg trajectory user user 2 is Guess- 2goods. is Guess- Therefore, > Samsung- > Samsung- > similarity Apple, > Apple, between trajectory user trajectory 1 user 3 user 3 should is 3Nike- isbe Nike- higher. > Puma- > Puma- Hence, > Adidas. > this Adidas. method Based Based is on on method not suitable used to for process door outdoor spaces. method used to process outdoor spaces, spaces, fluence fluence floors floors is elimated, is elimated, similarity similarity among among shapes shapes door door planar trajectories planar trajectories is measured. is measured. The results The results show that show that trajectories trajectories user 1 user user 1 2 user are 2more are more similar. similar. However, However, user user 1 1 user user 3 are 3 areboth bothterested terested buyg sportg goods. goods. Therefore, similarity similarity between between user user 1 1 user user 3 should 3 should be higher. be higher. Hence, Hence, this this method method is not is suitable not suitable for door for door spaces. spaces.

15 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, Multi-granularity trajectory. The triangles, circles, rectangles, pentagons denotes users 1, 1, 2, 2, 3, 3, 4, 4, respectively:(a) The shapes door planar trajectories is is not suitable for for evaluatg user similarity;(b) Usg only coarse-graed formation can t reflect differences visually;(c) Usg only fe-graed hierarchy will cause measurement similarity between users to to fall fall to to aa local local trap; trap;(d) Multi-granularity trajectory is is consistent with actual situation. Usg only coarse-graed hierarchy will cause accuracy actual similarity. As Usg only coarse-graed hierarchy will cause accuracy actual similarity. shown 14B coarse-graed hierarchy, cellular space is related to a certa As shown 14B coarse-graed hierarchy, cellular space is related to keyword. Clearly, four users have similar consumption habit y are all terested a certa keyword. Clearly, four users have similar consumption habit y are shoppg. However, differences between users are not visually reflected. In fe-graed all terested shoppg. However, differences between users are not visually reflected. hierarchy, similarity between users can be accurately measured. As shown In fe-graed hierarchy, similarity between users can be accurately measured. 14C, fe-graed hierarchy, it s obvious that user 1 user 3 are both terested As shown 14C, fe-graed hierarchy, it s obvious that user 1 user 3 are buyg sportg goods, which is consistent with ir actual behavior. However, numerous trajectories both terested buyg sportg goods, which is consistent with ir actual behavior. However, door movg s exist. Usg only fe- graed hierarchy will cause numerous trajectories door movg s exist. Usg only fe- graed hierarchy measurement similarity between users to fall to a local trap. As shown 14C, user 4 will cause measurement similarity between users to fall to a local trap. As shown visits Apple store when shoppg for sportg goods. Based on longest common subsequence 14C, user 4 visits Apple store when shoppg for sportg goods. Based on longest algorithm [56], similarity between user 1 user 4 is relatively low, which is consistent with common subsequence algorithm [56], similarity between user 1 user 4 is relatively low, which actual situation. In this work, MGSH-tree is employed to process trajectory sequences establish is consistent with actual situation. In this work, MGSH-tree is employed to process trajectory a dex for both coarse- fe-graed hierarchy models to improve sequences establish a dex for both coarse- fe-graed hierarchy recognition users behavior. As shown 14D, users trajectories conta multigranularity formation. User 3 is most similar to user 1, user 4 is second most similar models to improve recognition users behavior. As shown 14D, users trajectories conta multi-granularity formation. User 3 is most similar to user 1, user 4 is to user 1, user 2 is least similar to user 1, which is consistent with actual situation. second most similar to user 1, user 2 is least similar to user 1, which is consistent with 15 describes algorithm for a trajectory query. The getlcslength function actual situation. returns length maximum common sequence between trajectory keyword sequence 15 describes algorithm for a trajectory query. The getlcslength function target keyword sequence : returns length maximum common sequence between trajectory keyword sequence target keyword sequence :

16 ISPRS Int. J. Geo-Inf. 2016, 5, 176 ISPRS Int. J. Geo-Inf. 2016, 5, 176 ISPRS Int. J. Geo-Inf. 2016, 5, The The trajectory trajectory query query algorithm. algorithm. 15. The trajectory query algorithm Experimental ExperimentalResults Results Analysis Analysis 5. Experimental Results Analysis This section verifies search, This section verifies search, update update expansion expansion efficiencies efficiencies MACSI MACSI through through aa series series This section verifies search, update expansion efficiencies MACSI through a series comparative experiments. processor comparative experiments. A A personal personal computer computer with with aa 3.6-GHz 3.6-GHz Intel Intel Core Core i i processor comparative experiments. A personal computer with environment a 3.6-GHz Intel Core i processor 4-GB rom-access memory was used as operatg program. The program 4-GB rom-access memory was used as operatg environment program. The program 4-GB rom-access memory was used as operatg environment program. The program was realized realized through through Java. Java. An was An adjacency adjacency matrix matrix was was established established based based on on plan plan aa 22-floor 22-floor was realized through Java. An was adjacency matrix was established based movg on plan a 22-floor buildg Tianj, Cha, used as simulated data. In addition, trajectories buildg Tianj, Cha, was used as simulated data. In addition, movg trajectories were were buildg Tianj, Cha, plan. was used as simulated data. plan In addition, movg trajectories were generated usg given generated usg given floor floor plan shows shows floor floor plan buildg buildg simulated simulated generated usg given floor plan. 16 shows floor plan buildg simulated positiong pots pots movg movgs. s.aashoppg shoppg center Beijg, Cha, selected as real-data realpositiong center Beijg, Cha, waswas selected as 2, as positiong pots environment. movg s. A shoppg center Beijg, Cha, was selected realdata experimental The shoppg center has a buildg area 180,000 m a busess 2 experimental environment. The shoppg center has a buildg area 180,000 m, a busess area 2 2, six dataexperimental environment. The shoppg center has a buildg area 180,000 m, a busess area 120,000 m aboveground floors four belowground floors. To support -related 2 120,000 m, six aboveground floors four belowground floors. To support -related queries, area 120,000 m2, six aboveground floors four belowground floors.established. To support Keywords -related queries, levelstore each was manually were level each store br wasbr manually established. Keywords were extracted queries, level each store br was manually established. Keywords were extracted from Wikipedia to establish an verted dex. In real-data environment, 60 movg from Wikipedia to establish an verted dex. In real-data environment, 60 movg s with extracted from Wikipedia to establish an verted dex. In real-data environment, 60 movg s with different backgrounds whoshoppg were freely shoppg were different ages, gendersages, genders backgrounds who were freely were selected, selected, ir door s with movg differenttrajectories ages, genders backgrounds who were freely shoppg were selected, ir door were obtaed. 17 shows architectural plan movg trajectories were obtaed. 17 shows architectural plan real environment real ir door movg trajectories were obtaed. 17 shows architectural plan real environment extracted records partial trajectories. extracted records partial trajectories. environment extracted records partial trajectories. 16. (A,B) Simulated floor plan positiong pots (A,B) (A,B) Simulated Simulated floor floor plan plan positiong positiongpots. pots.

17 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, (A,B) Floor plan real environment trajectories movg s Experimental Results Usg Simulated Dataset The performed queries on simulated dataset are shown Table Considerg impact number cells cells s son on query query update update efficiencies, efficiencies, a sgle a sgle variable variable was was used used for for each each group group experiments. experiments. To To simulate simulate environments environmentsrangg ranggfrom fromsmall buildgsto large-scale commercial centers, number cells was set to ; cells were extracted or copied from simulated data. When number cells varied, number movg s wasset setto to When number movg s varied, number cells was set to To simulate low- to high-congestion conditions, number s was set to 10 10,000. The mean value 10 runs was used as as result resultfor foreach eachgroup group experiments. experiments. For For cells cells s s queries, queries, MACSI MACSI was was compared compared with with ITD-tree ITD-tree SI SI terms terms query query update efficiencies based on coarse- fe-graed cells s queries. For For trajectory query, MACSI was compared with SI terms complex trajectory query performance. Fally, memorycost costfor for MACSI, MACSI, ITD-tree ITD-tree SI were SI were compared. compared. The results The results show show that when that when processg processg cells cells -related -related queries, queries, MACSI MACSI not not only onlymatas matasits its spatial connectivity search capability but also has better search update efficiencies for for queries. In addition, MACSI MACSI can can also also support support multi-granularity multi-granularity queries, queries, memory memory cost cost can meet can meet practical practical requirements requirements application. application Fe-Graed Semantic Cell Query As shown 18, when number cells creases from 10 to 3000, query efficiency MACSI is superior to those SI ITD-tree, query efficiencies SI ITD-tree decrease significantly for followg reason: The SI ITD-tree do not consider needs fe-graed queries must traverse all nodes. In contrast, MACSI uses an verted dex for fe-graed ells, cells, an an crease number number cells cells will will not not significantly significantly affect affect MACSI. MACSI. As shown As shown 19, when 19, when number number s creases s creases from 10 from to 10,000, to 10,000, search time search time MACSI MACSI is mataed is mataed with with range range s, s, its query its query efficiency efficiency is superior is superior to those to those SI SI ITD-tree. ITD-tree. The reason The reason is that when is that when number number cells is cells fixed, is fixed, structural structural hierarchy hierarchy MACSI MACSI is relatively is relatively stable. stable. In addition, In addition, because because cell cell queries queries are not are significantly not significantly related related to tonumber number s, s, query query efficiencies efficiencies SI SIITD- ITD-tree are also are also relatively relatively stable. stable.

18 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, The effect cell number on fe-graed cell query. 18. The effect cell number on fe-graed cell query. 18. The effect cell number on fe-graed cell query. 19. The effect number on fe-graed cell query. 19. The effect number on fe-graed cell query. 19. The effect number on fe-graed cell query Coarse-Graed Semantic Cell Query AsCoarse-Graed shown Semantic 20, as Cell number Query cells creases, query efficiency MACSI is comparable As shown to that SI, 20, as both number are more efficient cells creases, than ITD-tree, query which efficiency is maly based MACSI on is followg comparable reasons. to The that The ITD-tree SI, ITD-tree does both does not are more not consider consider needs efficient than needs ITD-tree, queries which queries must is maly traverse based must on traverse all nodes, followg all resultg nodes, reasons. resultg a low The ITD-tree a low does query efficiency. not consider query efficiency. In comparison, needs In comparison, nodes queries nodes SI must MACSI traverse MACSI are both all are capable nodes, both resultg capable coarse-graed coarse-graed cell a low queries, query efficiency. cell queries, far fewer In comparison, nodes far fewer are searched nodes nodes are by searched SI SI by MACSI MACSI are than both MACSI by capable than ITD-tree. by coarse-graed Similar ITD-tree. to fe-graed Similar to fe-graed cell cell queries, query, far fewer cell number query, nodes are number s exerts searched by s a negligible SI exerts effect MACSI a negligible on coarse-graed than by effect ITD-tree. on coarse-graed cell query. Similar to As shown fe-graed cell query. As cell shown 21, as query, number number 21, as s s number creases, exerts s query a negligible creases, efficiency effect on query MACSI coarse-graed efficiency is comparable MACSI to that cell is query. comparable SI, As shown to that efficiencies SI, 21, as both efficiencies are superior number s both to that are creases, superior ITD-tree. to query that The efficiency query ITD-tree. efficiencies The MACSI query is efficiencies MACSI, SI comparable to that MACSI, ITD-tree SI, SI are all ITD-tree relatively efficiencies are stable. all relatively both are stable. superior to that ITD-tree. The query efficiencies MACSI, SI ITD-tree are all relatively stable.

19 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS ISPRS Int. J. Int. Geo-Inf. J. Geo-Inf. 2016, 2016, 5, 176 5, The effect cell number on coarse-graed cell query performance. 20. The effect cell number on coarse-graed cell query performance. 20. The effect cell number on coarse-graed cell query performance. 21. The effect number on coarse-graed cell query performance. 21. The effect number on coarse-graed cell query performance. 21. The effect number on coarse-graed cell query performance Fe-Graed Fe-Graed Semantic Semantic Object Object Query Query Fe-Graed Semantic Object Query As As shown shown 22, 22, when when number cells creases from 10 to 3000, fe-graed As shown query query efficiency 22, when MACSI MACSI number is relatively is cells creases stable stable from superior 10 to to 3000, to those those fe-graed ITD-tree SI, which SI, which decrease query decrease significantly. efficiency TheMACSI ma ma reason is relatively reason for for this stable this behavior superior is is that to those MACSI dexes ITD- tree tree s SI, which usg decrease an an verted significantly. dex, The whereas ma reason SI for this ITD-tree behavior do is that not have MACSI fe-graed dexes dexg s capabilities. usg an verted Thus, creases dex, whereas number SI ITD-tree cells will do crease not have fe-graed numbers nodes nodes dexg hierarchical capabilities. depths Thus, creases SI SI ITD-tree. number As shown cells will crease 23, as as numbers number s s nodes creases, creases, hierarchical query query efficiency depths SI MACSI ITD-tree. is is superior As shown to those ITD-tree 23, as number SI SI is is stable. s The creases, query efficiency query efficiency ITD-tree is MACSI superior is superior to that to those SI, primarily ITD-tree because SI tree stable. uses The delta query crement efficiency updates ITD-tree deletes is superior redundant to that movg s SI, primarily durg because -update ITD- is stable. The query efficiency ITD-tree is superior to that SI, primarily because ITD-tree uses delta crement updates deletes redundant movg s durg -update process. process. tree uses Thus, delta crement number updates nodes deletes that redundant ITD-tree movg must s traverse durg is relatively -update Thus, number nodes that ITD-tree must traverse is relatively low. In comparison, low. In process. Thus, number nodes that ITD-tree must traverse is relatively low. In number movg nodes SI contues to crease, its query efficiency will contuously decrease as number s creases.

20 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, comparison, number movg nodes SI contues to crease, its query comparison, number movg nodes SI contues to crease, its query ISPRS efficiency Int. J. Geo-Inf. will contuously 2016, 5, 176 decrease as number s creases efficiency will contuously decrease as number s creases. 22. The effect cell number on fe-graed query performance. 22. The effect cell number on fe-graed query performance. 23. The effect number on fe-graed query performance. 23. The effect number on fe-graed query performance. 23. The effect number on fe-graed query performance Coarse-Graed Semantic Object Query Coarse-Graed Semantic Object Query As Coarse-Graed shown Semantic 24, asobject number Query cells creases, similar to fe-graed cell query, As shown structural query 24, efficiency as number MACSI cells creases, is comparable similar with to fe-graed that SI, both cell As shown 24, as number cells creases, similar to fe-graed cell are query, more efficient structural than query ITD-tree. efficiency As shown MACSI is comparable 25, as with number that s SI, gradually both are query, structural query efficiency MACSI is comparable with that SI, both are creases, more efficient query than efficiency ITD-tree. As MACSI shown is comparable 25, as with number that s SI. Furrmore, gradually creases, query more efficient than ITD-tree. As shown 25, as number s gradually creases, efficiencies query efficiency both decrease significantly, MACSI is whereas comparable that with that ITD-tree remas SI. Furrmore, relatively stable, which query efficiencies query efficiency both decrease MACSI significantly, is comparable whereas with that that ITD-tree SI. remas Furrmore, relatively query is maly because ITD-tree has a stable hierarchical structure when number cells isstable, fixed. efficiencies which is maly both because decrease ITD-tree significantly, has a whereas stable hierarchical that structure ITD-tree when remas number relatively stable, In addition, ITD-tree uses delta crement updates deletes redundant movg s cells is which fixed. is In maly addition, because ITD-tree ITD-tree uses delta has a crement stable hierarchical updates structure deletes when redundant number movg cells s is a timely fashion durg -update process, whereas MACSI SI do not. Unlike fixed. a timely In addition, fashion durg ITD-tree uses -update delta crement process, updates whereas deletes MACSI redundant SI movg do not. s cell queries, queries require traversg more nodes, reby decreasg Unlike a timely cell fashion queries, durg -update queries process, require whereas traversg MACSI more SI do nodes, not. reby Unlike queries efficiency. decreasg cell queries, queries efficiency. queries require traversg more nodes, reby decreasg queries efficiency.

21 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, The The effect effect cell cell number number on on coarse-graed coarse-graed query query performance. performance The The effect effect number number on on coarse-graed coarse-graed query query performance. performance Complex Semantic Trajectory Query As shown 26, as as scale cells creases, complex trajectory query efficiency MACSI MACSIis issignificantly significantlysuperior superiorto to tothat that that SI SI SI also also also exhibits exhibits exhibits good good good stability. stability. stability. As As As shown shown shown 27, 27, 27, as as as scale scale s s creases, creases, MACSI MACSIis is is comparableto to SI when number s s is is is relatively relatively low low low but but but is significantly is is significantly superior superior superior once once once number number number s s s reaches reaches reaches Indeed, Indeed, Indeed, when processg when when processg processg complex complex complex trajectory trajectory trajectory query, query, MACSI hasmacsi both coarse-graed has has both both coarse- coarse- fe-graed fe-graed fe-graed dexes can dexes dexes accurately locate can can accurately accurately locate locate level reducelevel traversal reduce reduce cost traversal traversal cost cost tree, reby relativelytree, tree, quickly reby reby fdgrelatively complex quickly quickly fdg fdg trajectories. complex complex In comparison, trajectories. trajectories. SI must traverse In In comparison, comparison, each SI SI keyword, must must traverse traverse resultg each each low querykeyword, efficiency. resultg resultg low low query query efficiency. efficiency.

22 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, The effect cell number on trajectory query performance. 26. The effect cell number on trajectory query performance. 27. The effect number on trajectory query performance. 27. The effect number on trajectory query performance. 27. The effect number on trajectory query performance Semantic Cell Keyword Update Efficiency Semantic Cell Keyword Update Efficiency As Semantic shown Cell Keyword 28, as Update number Efficiency cells creases, cell keyword update As shown 28, as number cells creases, cell keyword update efficiency As shown MACSI is superior 28, as tonumber SI ITD-tree cells creases, efficiencies. Increasg cell keyword number update cells efficiency MACSI is superior to SI ITD-tree efficiencies. Increasg number cells results efficiency crements MACSI is superior hierarchical to structures SI ITD-tree ITD-tree efficiencies. SI. Increasg Consequently, number number cells results crements hierarchical structures ITD-tree SI. Consequently, number cell results nodes crements that must be traversed hierarchical creases. structures In contrast, ITD-tree MACSI usessi. a hash Consequently, dex for fe-graed cell nodes that must be traversed creases. In contrast, MACSI uses a hash dex for number fegraed cell nodes dexg that dexg must can be ensure traversed relatively can ensure creases. high update relatively In contrast, efficiency. high update MACSI As shown efficiency. uses As a hash shown dex 29, as for scale fegraed s 29, as scale creases, dexg update s creases, can efficiency ensure update relatively MACSI efficiency high update is superior MACSI efficiency. to those is superior As shown ITD-tree to those 29, SI. In ITD-tree as addition, scale SI. update In s efficiencies addition, creases, update MACSI, update ITD-tree efficiencies efficiency SI MACSI, are MACSI relatively ITD-tree is superior stable, which SI to are those is maly relatively because stable, ITD-tree which update is SI. maly In addition, because cell update keywords update efficiencies is not significantly cell keywords MACSI, related ITD-tree to s. is not significantly SI are related relatively to stable, s. which is maly because update cell keywords is not significantly related to s.

23 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, The effect cell number on update performance. 28. The effect cell number on update performance. 29. The effect number on update performance. 29. The effect number on update performance. 29. The effect number on update performance Memory Cost Memory Cost 30 shows a comparison memory cost for different dex structures with varyg numbers cells. 30 shows As As a comparison number cells creases, memory cost for memory different costs dex MACSI, structures with SI varyg ITD-tree numbers crease cells. significantly. As number The The memory cells memory creases, cost cost MACSI memory MACSI is costs higher is higher than than MACSI, that that SI SI SI ITD-tree, ITD-tree, crease significantly. ITD-tree ITD-tree has has The best memory best performance. performance. cost This MACSI This maly ishigher maly because than because that MACSI MACSI has has capacity ITD-tree, capacity to dex to dex both ITD-tree both has best unit unit performance. spaces spaces through through This is maly MAC-tree, because MGSI MACSI multiple has auxiliary capacity tables, to dex both cost which is is unit needspaces for more through memory space MAC-tree, to support MGSI dex structure multiple auxiliary strategy, tables, which which iscost a typical a typical which space-for-time space-for-time is need strategy. for more strategy. However, memory However, space MACSI to support MACSI still controls still dex controls structure memory memory cost relatively strategy, cost relatively well. which When is well. a typical re When are space-for-time re 3000are cells, 3000 strategy. cells, memory However, memory cost is only cost 1.4 is MACSI only Mb, dicatg 1.4 still Mb, controls dicatg that that MACSI memory still MACSI cost performs relatively still performs well well. When terms well re terms memory 3000 memory cost cells, for buildg cost memory for buildg structures cost is structures for only large-scale 1.4 for Mb, large-scale dicatg busess busess centers. that centers. MACSI 31 still shows performs 31 shows memory well cost memory terms as a function cost memory as a function cost number for buildg number s. structures Similar s. for to large-scale Similar pattern to for busess pattern change centers. for change memory 31 cost memory withmemory cost number with cost as number a cells, function cells, memory memory cost cost s. MACSI Similar MACSI to SI creases pattern SI creases for significantly change significantly for memory creasg for an creasg cost number with number s. s. Incells, comparison, In memory comparison, cost memory memory MACSI cost cost ITD-tree SI ITD-tree creases is relatively is significantly relatively low low stable, for which stable, creasg is which similar number is similar to s. pattern to pattern In shown comparison, shown 21. memory This21. This maly cost is maly because ITD-tree because ITD-tree is relatively ITD-tree useslow delta uses crement stable, delta crement which updates is similar updates deletes to redundant pattern deletes shown redundant movg s movg s This is maly a timely because fashion. ITD-tree Based on uses delta aforementioned crement updates experimental deletes results redundant from movg s a timely fashion. Based on aforementioned experimental results from

24 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS Int. J. Geo-Inf. 2016, 5, perspective a timely fashion. space Based consumption, aforementioned MACSI experimental tegrates results space from cell perspective space needs space perspective more consumption, memory space compared MACSI consumption, tegrates to ITD-tree MACSI space tegrates SI, cell although space it space still needs performs more cell memory space well for compared actual needs more application to memory ITD-tree scenarios compared SI, terms although to memory ITD-tree it stillcosts. performs well SI, although for actualit application still performs scenarios well for terms actual application memory costs. scenarios terms memory costs. 30. The effect cell number on memory costs. 30. The effect cell number on memory costs. 31. The effect number on memory costs. 31. The effect number on memory costs Results Experiments Usg Real Dataset 5.2. Results Experiments Usg Real Dataset 32 shows results results for for cells, cells, s, s, trajectory trajectory queries queries updates updates listed listed Table 32 shows 3Table for 3 for real results data real for data environment. For cells, For fe-graed s, trajectory queries queries, MACSI updates only requires listed 16Table msto to3 query for a areal specific data environment. movg For fe-graed 7 ms 7 ms to to query query a specific a specific queries, MACSI cell. cell. In only In comparison, requires due 16 due ms to to to query lack lack a specific capacity movg to to execute fe-graed 7 ms to query a specific queries, SI cell. In comparison, ITD-tree require due more to than lack 2 s to execute capacity a specific to execute fe-graed cell query more queries, than 1 ssi to execute ITD-tree a specificrequire more than query. 2 s to execute Clearly, a specific MACSI has better cell query performance more than 1 fe-graed s to execute a -related specific queries. query. For coarse-graed Clearly, MACSI -related has better queries, query performance MACSI is fe-graed significantly -related advantageous over queries. ITD-tree For coarse-graed comparable -related to to SI SI terms queries, terms performance. MACSI The is significantly MACSI The MACSI only advantageous requires only requires 192 ms 192 over to ms execute toitd-tree execute a a coarse-graed comparable to movg SI movg terms performance. query query 16 The 16 ms ms MACSI to to execute only a requires coarse-graed 192 ms to execute cell a coarse-graed query, whereas ITD-tree movg has particularly query low 16 ms coarse-graed to execute a coarse-graed query execution cell efficiency. query, For whereas trajectory ITD-tree queries, has particularly specific low coarse-graed trajectory query execution efficiency. For trajectory queries, specific trajectory

25 ISPRS Int. J. Geo-Inf. 2016, 5, ISPRS a coarse-graed Int. J. Geo-Inf. 2016, 5, 176 cell query, whereas ITD-tree has particularly low coarse-graed query execution efficiency. For trajectory queries, specific trajectory query query efficiency efficiency creases creases by over by one over fold one when fold usg when usg structure structure proposed proposed present present study study compared compared to SI. to ForSI. For update-related update-related operations, operations, MACSI MACSI only requires only requires 4 ms to execute 4 ms to execute a a update operation, update operation, which is better which than is better SI than (145 ms) SI (145 ms) ITD-tree (165 ITD-tree ms). The (165 MACSI ms). The has better MACSI performance has better performance update operations. update operations. 32. Real dataset result. (ITD-Tree, Si MACSI are distributed abscissa axis, respectively. 32. Real dataset result. (ITD-Tree, Si MACSI are distributed abscissa axis, It is obvious that overall trend system response time is ITD-Tree > SI > MACSI. Additionally, respectively. It is obvious that overall trend system response time is ITD-Tree > SI > MACSI. MACSI showed better performance than ITD-Tree SI cells, s queries as well Additionally, MACSI showed better performance than ITD-Tree SI cells, s as updates). queries as well as updates). To demonstrate reliability reliability improvement improvement from usg from MACSI usg tomacsi extend sgle-floor to extend applications sgle-floor applications to multi-floor to door multi-floor spaces door usgspaces spatial usg syntax spatial syntax caloric costs, caloric a movg costs, a movg is located at is located a certaat location a certa location real data environment, real data environment, 10-nearest 10-nearest cells are identified cells are (e.g., identified 10-nearest (e.g., 10-nearest lavatories lavatories O1; to position O1; position movg movg search results search results are shown are shown 33). The 33). The actual actual arrival arrival time time is measured is usg usg timers mobile phones. Tables 6 7 compare actual arrival times among MACSI, ITD-tree SI. SI. As As shown Table Table 6, 6, actual actual arrival arrival time time from from location movg to to D is is 47 s. s. By comparison, B C, which are located on same floor as movg, take 75 s 105 s, respectively. ITD-tree SI are dexes based on a sgle-floor door space. When se dexes search spatial space (e.g., a k-nearest neighbor search), floor floor where where movg movg is located is located will will be searched be searched first, followed first, followed by different by different floors, floors, thus, thus, rankg rankg result result ITD-Tree SI SIis is B-C-D, which is unreliable. In comparison, MACSI corporates door cells on different floors to a unified dex, its rankg result is D-B-C (as shown Table 7), which is more reliable. As anor example, ITD-tree SI place J (located on 5th floor) at end sequence even though actual arrival time to move from location movg to to J requires J only only s, s, which which is superior is to to or or locations (e.g., (e.g., G, G, H, H, I). By I). By analyzg analyzg or or sortg sortg results results shown shown Tables Tables 6 6 7, we 7, can we can clearly clearly conclude conclude that that search search results results MACSI MACSI are more are comprehensive more comprehensive reliable reliable than dexes than dexes based onbased sgle-floor on sgle-floor door spaces. door spaces.

26 ISPRS ISPRS Int. Int. J. J. Geo-Inf. 2016, 2016, 5, 5, The positions movg locations search results. (The black humanoid 33. The positions movg locations search results. (The black humanoid is location movg, (A J) denote 10-nearest lavatories to movg ; is location movg, (A J) denote 10-nearest lavatories to movg ; (A C) are located on 3rd floor; (D F) are on 2nd floor; (G I) are 4th floor; (J) is on (A C) are located on 3rd floor; (D F) are on 2nd floor; (G I) are 4th floor; (J) is on 5th 5th floor.) floor.) Table Table 6. The 6. The actual actual arrival times ITD-Tree SIto to 10-nearest lavatories real real dataset. dataset. Order Order Floor Floor Number Number Destation Destation Time Time 1 3 A 22 s 1 3 A 22 s B B 75 s75 s C C 105 s105 s D D 47 s47 s 5 2 E 135 s 5 2 E 135 s 6 2 F 165 s 7 4 G 46 s 8 4 H 132 s 9 4 I 172 s 10 5 J 70 s

27 ISPRS Int. J. Geo-Inf. 2016, 5, Table 7. The actual arrival times MACSI to 10-nearest lavatories real dataset. Order Floor Number Destation Time 1 3 A 22 s 2 2 D 47 s 3 4 G 46 s 4 3 B 75 s 5 5 J 70 s 6 3 C 105 s 7 2 E 135 s 8 4 H 132 s 9 2 F 165 s 10 4 I 172 s For memory costs, MACSI memory cost is 238 kb for real data, SI is 117 kb, ITD-tree is 68 kb. Similar to simulated data, MACSI consumes more memory than ITD-tree SI, although its memory cost is still mataed at a low level. In addition, or experimental parameters were observed, e.g., itialization node sertion processes MACSI are relatively complex. The execution time required for itialization node sertion process MACSI are fairly long. Therefore, MACSI is suitable for applications that are sensitive to itialization sertion time but sensitive to real-time queries. 6. Conclusions Outlook The MACSI exps sgle-floor door adjacency cellular spaces. In addition, it subdivides open cells (e.g., hallways lobbies) usg space syntax to ensure reasonableness adjacency cellular spaces to optimize connected cells (e.g., stairs elevators) based on caloric cost. Given specific needs door queries, present study proposes a MGSH-tree uses verted dexg to improve query efficiency expansion capability. Furrmore, a formal representation for door trajectories based on MGSH-tree is proposed, trajectories movg s are dexed. A comparative analysis MACSI, ITD-tree SI usg simulated-data real-data environments confirmed that MACSI exps application dexg from sgle-floor door spaces to multi-floor door spaces provides more accurate spatial query results. In addition, MACSI has better spatial sematic query performance, lower update costs, better expansion capability. In addition, MACSI uses auxiliary tables to combe cellular spaces; thus, MACSI s memory cost is higher than that ITD-tree SI, although it still has a good memory cost control capability, which can meet practical requirements certa applications. Currently, several studies addressg dexg door movg s rema to be completed. We plan to make improvements followg areas future. Future research could consider dynamic adjacency matrices to adapt to structural changes buildgs. Additionally, an outdoor Euclidean space could be seamlessly connected with an door cellular space to realize tegrated dexg door outdoor movg s. We only consider response time memory cost current evaluation. In future, we can learn from ideas applied big data applications [57], which collect user teraction data from mobile phones n evaluate dices from different angles, such as user satisfaction, actual arrival time, or dicators. Acknowledgments: This study was supported by National Science-technology Support Plan Cha (Grant No. 2015BAJ02B00), Youth Foundation Institute Remote Sensg Digital Earth, CAS (Y5SJ1100CX). Author Contributions: Hui L, Lg Peng Tianhe Chi had origal idea for study; Hui L Tianyue Liu designed experiments; Hui L Si Chen performed experiments; Hui L, Lg Peng Si Chen wrote paper. Conflicts Interest: The authors declare no conflict terest.

28 ISPRS Int. J. Geo-Inf. 2016, 5, References 1. Klepeis, N.E.; Nelson, W.C.; Ott, W.R.; Robson, J.P.; Tsang, A.M.; Switzer, P.; Behar, J.V.; Hern, S.C.; Engelmann, W.H. The national human activity pattern survey (NHAPS): A resource for assessg exposure to environmental pollutants. J. Expo. Anal. Environ. Epidemiol. 2001, 11, [CrossRef] [PubMed] 2. Subway, B. Passenger Flow Information. Available onle: (accessed on 7 March 2016). 3. Petrenko, A.; Bell, S.; Stanley, K.; Qian, W.; Sizo, A.; Knowles, D. Human Spatial Behavior, Sensor Informatics, Disaggregate Data; Sprger: Cham, Switzerl, Schougaard, K.R.; Grønbæk, K.; Scharlg, T. Indoor Pedestrian Navigation Based on Hybrid Route Planng Location Modelg; Sprger: Berl, Germany, Liu, T.; Chi, T.; Li, H.; Rui, X.; L, H. A GIS-oriented location model for supportg door evacuation. Int. J. Geogr. Inf. Sci. 2014, 29, [CrossRef] 6. Want, R. Rfid explaed: A Primer on Radio Frequency Identification Technologies. In Synsis Lectures on Mobile & Pervasive Computg; Morgan & Claypool Publishers: San Rafael, CA, USA, Bahl, P.; Padmanabhan, V.N. Radar: An -buildg RF-based user location trackg system. In Proceedgs Neteenth Annual Jot Conference IEEE Computer Communications Societies (INFOCOM 2000), Tel Aviv, Israel, March Bell, S.; Jung, W.R.; Krishnakumar, V. Wifi-Based Enhanced Positiong Systems: Accuracy through Mappg, Calibration, Classification. In Proceedgs 2nd ACM Sigspatial International Workshop on Indoor Spatial Awareness, San Jose, CA, USA, 3 5 November Wheeler, A. Commercial applications wireless sensor networks usg zigbee. IEEE Commun. Mag. 2007, 45, [CrossRef] 10. J, P.Q.; Na, W.; Zhang, X.X.; Yue, L.H. Movg data management for door spaces. Ch. J. Comput [CrossRef] 11. Berry, P.L.J.; Bell, S. Potg accuracy: Does dividual potg accuracy differ for door vs. Outdoor locations? J. Environ. Psychol. 2014, 38, [CrossRef] 12. Bell, S.; Wei, T.; Jung, W.R.; Scott, A. A conceptual model trust for door positiong systems. In Proceedgs 3rd ACM Sigspatial International Workshop on Indoor Spatial Awareness, Chicago, IL, USA, 1 4 November Wei, T.; Bell, S. Impact Indoor Location Information Reliability on Users Trust an Indoor Positiong System; Sprger: Berl/Heidelberg, Germany, Alamri, S.; Taniar, D.; Safar, M.; Al-Khalidi, H. Spatiotemporal dexg for movg s an door cellular space. Neurocomputg 2013, 122, [CrossRef] 15. Jensen, C.S.; Lu, H.; Yang, B. Indexg trajectories movg s symbolic door space. In Proceedgs 11th International Symposium (SSTD 2009), Aalborg, Denmark, 8 10 July Alamri, S.; Taniar, D.; Safar, M. Indexg movg s door cellular space. In Proceedgs th International Conference on Network-Based Information Systems (NBiS), Melbourne, Australia, September 2012; pp Alamri, S.; Taniar, D.; Safar, M.; Al-Khalidi, H. A connectivity dex for movg s an door cellular space. Pers. Ubiquitous Comput. 2014, 18, [CrossRef] 18. Ben, T.; Q, X.; Wang, N. A -based dexg for door movg s. Int. J. Distrib. Sens. Netw. 2014, 2014, [CrossRef] 19. Šaltenis, S.; Jensen, C.S.; Leutenegger, S.T.; Lopez, M.A. Indexg positions contuously movg s. In Proceedgs ACM International Conference on Management Data Symposium on Prciples Database Systems, Dallas, TX, USA, May Tao, Y.; Papadias, D.; Sun, J. The TPR*-tree: An optimized spatio-temporal access method for predictive queries. In Proceedgs 29th International Conference on Very Large Data Bases, Berl, Germany, 9 12 September 2003; pp Tao, Y.; Papadias, D. MV3R-tree: A spatio-temporal access method for timestamp terval queries. In Proceedgs 27th International Conference on Very Large Data Bases (VLDB 2001), Roma, Italy, September 2001; pp

29 ISPRS Int. J. Geo-Inf. 2016, 5, Nascimento, M.A.; Silva, J.R.O. Towards historical R-trees. In Proceedgs 1998 ACM Symposium on Applied Computg, Atlanta, GA, USA, 27 February 1 March 1998; pp Pfoser, D.; Jensen, C.S.; Theodoridis, Y. Novel approaches query processg for movg trajectories. In Proceedgs 26th International Conference on Very Large Data Bases (VLDB 2000), Cairo, Egypt, September 2000; pp Frentzos, E. Indexg s movg on fixed networks. In Proceedgs International Symposium on Advances Spatial Temporal Databases (SSTD 2003), Santori Isl, Greece, July 2003; pp Almeida, V.T.D. Indexg trajectories movg s Networks. In Proceedgs 16th International Conference on Scientific Statistical Database Management, Santori Isl, Greece, June Dg, Z.M. An dex structure for frequently updated network-constraed movg trajectories. Ch. J. Comput. 2012, 35, [CrossRef] 27. Vanclooster, A.; Nico, V.D.W.; De Maeyer, P. Integratg door outdoor spaces for pedestrian navigation guidance: A review. Trans. GIS 2016, 20, [CrossRef] 28. Worboys, M. Modelg door space. In Proceedgs 3rd ACM SIGSPATIAL International Workshop on Indoor Spatial Awareness (ISA 2011), Chicago, IL, USA, 1 4 November 2011; pp Zlatanova, S.; Sithole, G.; Nakagawa, M.; Zhu, Q. Problems door mappg modellg. ISPRS 2013, XL-4/W4, [CrossRef] 30. Kim, J.S.; Kang, H.Y.; Lee, T.H.; Li, K.J. Topology prism model for 3D door spatial s. In Proceedgs Tenth International Conference on Mobile Data Management: Systems, Services Middleware, Taipei, Taiwan, May 2009; pp Elfes, A. Usg occupancy grids for mobile robot perception navigation. Computer 1989, 22, [CrossRef] 32. Demyen, D.; Buro, M. Efficient triangulation-based pathfdg. In Proceedgs 23rd AAAI Conference on Artificial Intelligence, Vancouver, BC, Canada, 2007; pp Mekni, M. Automated Generation Geometrically-Precise Semantically-Informed Virtual Geographic Environments Populated with Spatially-Reasong Agents; Universal-Publishers: Boca Raton, FL, USA, Wallgrün, J.O. Hierarchical Voronoi Graphs; Sprger: Berl/Heidelberg, Germany, Pennga, F.; Oosterom, P.V.; Kazar, B.M. A Tetrahedronized Irregular Network Based DBMS Approach for 3D Topographic Data Modelg; Sprger: Berl/Heidelberg, Germany, Zhao, F.; Luo, H.Y.; L, Q.; Yan, M.A. Node localization algorithm based on kernel function Markov chas. J. Commun. 2010, 31, Jensen, C.S.; Lu, H.; Yang, B. Graph model based door trackg. In Proceedgs Tenth International Conference on Mobile Data Management (MDM 2009), Taipei, Taiwan, May 2009; pp Yang, B.; Lu, H.; Jensen, C.S. Probabilistic threshold K nearest neighbor queries over movg s symbolic door space. In Proceedgs International Conference on Extendg Database Technology (EDBT 2010), Lausanne, Switzerl, March 2010; pp Yuan, W.; Schneider, M. Supportg contuous range queries door space. In Proceedgs 2010 Eleventh International Conference on Mobile Data Management, Kansas City, MO, USA, May 2010; pp Kang, H.Y.; Kim, J.S.; Li, K.J. Strack: Trackg door symbolic space with RFID sensors. In Proceedgs 18th SIGSPATIAL International Conference on Advances Geographic Information Systems, San Jose, CA, USA, 2 5 November 2010; pp Becker, T.; Nagel, C.; Kolbe, T.H. A multilayered space-event model for navigation door spaces. In 3D Geo-Information Sciences; Sprger: Berl/Heidelberg, Germany, 2008; pp Li, X.; Claramunt, C.; Ray, C. A grid graph-based model for analysis 2D door spaces. Comput. Environ. Urban Syst. 2010, 34, [CrossRef] 43. Zlatanova, S.; Liu, L.; Sithole, G. A conceptual framework space subdivision for door navigation. In Proceedgs 5th ACM Sigspatial International Workshop on Indoor Spatial Awareness, Orlo, FL, USA, 5 8 November 2013; pp Zlatanova, S.; Liu, L.; Sithole, G.; Zhao, J.; Mortari, F.; Liu, L.; Sithole, G.; Zhao, J.; Mortari, F. Space Subdivision for Indoor Applications; Delft University Technology: Delft, The Nerls.

30 ISPRS Int. J. Geo-Inf. 2016, 5, Sh, S.S.; Kim, G.; Bae, H.Y. Adaptive cell-based dex for movg s door. Ksii Trans. Internet Inf. Syst. 2012, 6, [CrossRef] 46. Hillier, B. Space Is Mache; Cambridge University Press: Cambridge UK, Jiang, B.; Claramunt, C. Integration space syntax to GIS: New perspectives for urban morphology. Trans. GIS 2002, 6, [CrossRef] 48. Jiang, B.; Claramunt, C.; Klarqvist, B. Integration space syntax to GIS for modellg urban spaces. Int. J. Appl. Earth Obs. Geof. 2013, 2, [CrossRef] 49. J, P.; Zhang, L.; Zhao, J.; Zhao, L.; Yue, L. Semantics modelg door movg s. Int. J. Multimed. Ubiquitous Eng. 2012, 7, Lymberopoulos, D.; Liu, J.; Yang, X.; Choudhury, R.R.; Hziski, V.; Sen, S. A realistic evaluation comparison door location technologies. In Proceedgs 14th International Conference on Information Processg Sensor Networks, Seattle, WA, USA, April 2015; pp Bassett, D.R.; Vachon, J.A.; Kirkl, A.O.; Howley, E.T.; Duncan, G.E.; Johnson, K.R. Energy cost stair climbg descendg on college alumnus questionnaire. Med. Sci. Sports Exerc. 1997, 29, [CrossRef] [PubMed] 52. Butts, N.K.; Dodge, C.; Mcalpe, M. Effect steppg rate on energy costs durg stairmaster exercise. Med. Sci. Sports Exerc. 1993, 25, [CrossRef] [PubMed] 53. Chuan, T.K.; Abdul Rashid, A. Heart rate, oxygen uptake, energy cost ascendg descendg stairs. Med. Sci. Sports Exerc. 2002, 34, Froelicher, V.F.; Myers, J. Effect exercise on heart prevention coronary heart disease Exercise heart (fifth edition) Chapter thirteen. Exerc. Heart 2006, Li, Q.; Zheng, Y.; Xie, X.; Chen, Y.; Liu, W.; Ma, W.Y. Mg user similarity based on location history. In Proceedgs 16th ACM SIGSPATIAL International Symposium on Advances Geographic Information Systems (ACM-GIS 2008), Irve, CA, USA, 5 7 November 2008; pp Rick, C. New algorithms for longest common subsequence problem. J. ACM 1977, 24, Liang, T.; Lai, H.; Ku, Y. Personalized content recommendation user satisfaction: Theoretical synsis empirical fdgs. J. Manag. Inf. Syst. 2006, 23, [CrossRef] 2016 by authors; licensee MDPI, Basel, Switzerl. This article is an open access article distributed under terms conditions Creative Commons Attribution (CC-BY) license (