Efficient Routing Algorithms Combining History and Social Predictors in Mobile Social Networks

Transcription

1 Effcent Routng Algorthms Combnng and Socal Predctors n Moble Socal Networks Xao Chen 1, Chengyn Lu 2, Cong Lu 2 1 Department of Computer Scence, Texas State Unversty, San Marcos, TX USA 2 Department of Computer Scence, Sun Yat-Sen Unversty, Guangzhou, Chna Emal: xc1@txstate.edu, luchyn@163.com, lucong3@mal.sysu.edu.cn Abstract A moble Socal Network (MSN) s a type of wreless networks formed by people movng around carryng moble devces. In ths paper, we specfcally study the MSNs that are formed mpromptu, e.g. when people gather together for a conference, event, or festval. We refer to them as Impromptu Moble Socal Networks (IMSNs), whch allow people to communcate n a lghtweght fashon based on contact opportuntes va local wreless bandwdth. In IMSNs, node connectons are tmedependent and short-term. The exstng MSN routng algorthms usng network analyss of socal network graphs and statc node socal features may not be sutable for IMSNs. Thus, we propose novel hybrd routng algorthms based on two tme-related factors node contact hstory and dynamc socal features to capture node moblty n IMSNs. We frst propose a hybrd algorthm called that makes a weghted combnaton of the hstory and the socal predctors based on these two factors. And then we upgrade t to by ntroducng a novel concept called socal crcle n the socal predctor to mprove message delvery. Smulaton results comparng our algorthms wth the exstng ones and wth the ones that only consder one factor show that our algorthms outperform the others n terms of delvery rato and latency wth a slght ncrease n the number of forwardngs. The results also confrm the effectveness of usng a node s socal crcle n our algorthms. Index Terms hstory-based, moble socal networks, routng, socal-based, socal features I. INTRODUCTION Moble Socal Networks (MSNs), formed by people movng around carryng moble devces such as smartphones, tablets, laptops, and so on, are becomng ubqutous n our daly lves. Dfferent from the popular socal networks lke Facebook [1] and LnkedIn [2], n ths paper, we study a specfc knd of MSNs that are formed mpromptu. We refer to them as Impromptu Moble Socal Networks (IMSNs). The IMSNs can be formed when people carryng moble devces attend a conference, event, or festval. The IMSNs allow people to communcate n a lghtweght mechansm based on contact opportuntes va local wreless bandwdth such as Bluetooth wthout a network nfrastructure. The lnks between nodes n IMSNs are tme-dependent and short-term and thus contnuous network connectvty s not guaranteed. Nodes n IMSNs communcate through a store-and-forward fashon. When two nodes move wthn each other s transmsson range, they communcate drectly and become neghbors durng that tme perod. When they move out of ther ranges, ther contact s lost. The message to be delvered needs to be stored n the local buffer untl a contact occurs n the next hop. Due to the uncertanty and tme-varyng nature of IMSNs, routng poses unque challenges: The conventonal ad-hoc network routng schemes, such as DSR [11], LAR [13], DSDV [16], AODV [17], etc., would fal. Routng n IMSNs requres a new model that conssts of a sequence of ndependent, local forwardng decsons, based on the current connectvty nformaton and the predctons of future connectvty to sut ts dstrbuted and dynamc nature. In IMSNs, routng algorthms can be measured by three performance metrcs. (1) Delvery rato. It s the fracton of generated messages that are successfully delvered to the destnaton. (2) Delvery latency. It s the tme between when a message s generated and when t s receved by the destnaton. (3). It s the number of forwardngs needed to delver a message to ts destnaton. An effcent routng algorthm should ental a hgh delvery rato and low latency wth an acceptable number of forwardngs. Despte ther smplcty, rudmentary approaches such as [25] where a message holder epdemcally sends a message to all of the nodes t contacts and [12] where a source only drectly delvers a message to the destnaton can stll work n IMSNs. But has a hgh cost of message forwardngs and can have a long latency. As mentoned above, the key to desgnng an effcent IMSN routng protocol s to have a good predctor for a message holder to locally dentfy a forwarder whch s most lkely to delver a message to the destnaton based on the message holder s current connectvty nformaton. In the lterature, researchers use dfferent current connectvty nformaton to predct the future connectvty. Some researchers generate socal network graphs by lnkng nodes wth past encounters and apply complex socal analyss methods based on node centralty and smlarty to predct nodes future meetng probabltes [5], [1]. To facltate dscusson, we refer to ths method as socal-analyss-based method. In ths method, a lnk n the socal network graph means that two nodes have met n the past, whch has predctve value for future contacts. Nonetheless, the aggregaton of contacts between nodes over tme nto a statc socal graph presents an nherent mappng tradeoff, where some nformaton about tmng of contacts s lost [9], [27]. Some other researchers use socal features n user profles as the current nformaton to predct future connectvty [14], [26]. We refer to ths method as socal-proflebased method. The socal features F 1, F 2, F 3, may refer

2 to people s natonalty, cty, language, etc. And f 1, f 2, f 3, represent the values of these socal features. For example, the value of language can be Englsh. In ths paper, for convenence s sake, when we menton comparng node socal features, we mean comparng the values of ther socal features. The ntuton of ths method s that people come n contact more frequently f they have more socal features n common. In each hop of the routng process, the message holder selects a node that has the most common socal features wth the destnaton as the next forwarder. The advantage of ths method s that t does not need to record node contact hstory. Nevertheless, t may not work well f users actvtes do not match the statc socal features n ther profles. For example, someone who puts New York as hs state n hs profle may actually attend a conference n Texas. In the IMSNs we dscuss n ths paper, where lnks between nodes are tme-dependent, we need to use nformaton, especally tme-related nformaton, that can capture users dynamc behavor to be used as the current nformaton to predct future connectvty. Thus, we consder two peces of nformaton: node contact hstory and dynamc socal features. Node contact hstory records the contact tmes of nodes when they move wthn each other s range. Node contact hstory s often used by researchers n desgnng varous utlty functons such as average number of contacts [3], number of tmes nodes met last [6], and elapsed tme snce last contact [22] n Delay Tolerant Network (DTN) routng protocols. As ponted out by [6], the hstory of contact between nodes contans valuable, but nosy nformaton about the current network topology. Dynamc socal features, relatve to the statc socal features n user profles, are used to capture nodes dynamc behavor. We frst ntroduced the dea n our paper [19]. In dynamc socal features, we not only record f a node has partcular socal feature values, but also record the frequency ths node has met other nodes whch have these socal feature values. For example, we not only record that a node A s a New Yorker and a Student, but also record that t has met New Yorkers 9% of the tme and Students 8% of the tme durng the tme nterval we observe. Unlke statc socal features from user profles, dynamc socal features are tme-related. So they change as user actvtes change over tme. And thus we can have a more accurate way to choose the next best forwarder. For example, suppose the destnaton has socal feature values New Yorker and Student and we have two canddate nodes A and B, both of whch are New Yorkers and Students. Nodes A and B are equally good forwarders f we just look at ther statc socal feature values. However, f we know that A has met New Yorkers 9% of the tme and Students 8% of the tme and B has met New Yorkers 6% of the tme and Students 4% of the tme durng the tme nterval we observe, then obvously A s a better forwarder. Based on the above dscusson, n ths paper, we wll use node contact hstory and dynamc socal features as the current nformaton and desgn effcent hybrd routng algorthms usng predctors combnng the hstory predctor based on the node contact hstory and the socal predctor based on the dynamc socal features. As far as we know, we are the frst to combne these two tme-related factors to capture the dynamc behavor of nodes to make routng decsons n IMSNs. We frst put forward a routng algorthm called whch selects the next best forwarder based on the weghted combnaton of the hstory and the socal predctors. In, the hstory predctor s obtaned by applyng lnear regresson to the node contact hstory wth the destnaton. And the socal predctor s calculated by utlzng socal smlarty metrcs derved from data mnng [8] on the dynamc socal features. Next, we upgrade to by ntroducng a novel concept called socal crcle n the socal predctor calculaton. A node s socal crcle here refers to a group of nodes that are socally smlar to ths node based on the dynamc socal features. In the socal predctor n, we not only consder the socal smlarty of a node wth the destnaton but also the meetng probablty and the socal smlarty of ths node wth the destnaton s socal crcle. The ntuton s that f a node s socally smlar to the destnaton or often meets a set of nodes that are socally smlar to the destnaton, then ths node wll have a hgher probablty to forward the message to the destnaton by tself or through one of the nodes n the destnaton s socal crcle. To evaluate the performance of our algorthms, we compare them wth the socal-analyss-based and socal-profle-based methods, and the pure hstory-based and pure dynamc-socalfeature-based algorthms that just adopt node contact hstory or dynamc socal features as the current nformaton by smulatons usng a real trace reflectng the scenaros of the IMSNs we dscuss. We mplement sngle-copy (only one copy of the message exsts n the network n the routng process) and mult-copy (multple copes of the message exst n the network n the routng process) versons of the algorthms. In both versons, the results consstently show that our algorthms outperform the exstng algorthms n terms of delvery rato and latency wth a slght ncrease n the number of forwardngs. Furthermore, the algorthm s shown to be better than due to the utlzaton of the socal crcle concept. These results demonstrate the effectveness of usng tme-related nformaton and a node s socal crcle n the routng algorthms for IMSNs. The rest of the paper s organzed as follows: Secton II references the related works; Secton III presents our routng algorthms; Secton IV explans the calculaton of the predctors; Secton V shows the smulaton results and the concluson and future work are n Secton VI. II. RELATED WORKS In ths secton, we reference some related routng algorthms n MSNs. The rudmentary and hstory-based approaches were orgnally developed for DTNs. But they can also be used n MSNs. The socal-based and hybrd approaches are desgned for the MSNs as they consder socal factors. A. Rudmentary Approaches One effcent yet costly routng approach n DTNs s [25] where a message holder forwards a message to all of

3 the hosts t meets. The opposte approach s [12], where the source just wats and sends the message to the destnaton drectly when they meet. It only has one forwardng but the latency can be very hgh. B. -based Approaches In DTN routng algorthms, several papers make routng decsons usng utlty functons based on the contact hstory of nodes. Dubos-Ferrere et al. [6] predct the nodes future meetng probablty by the number of tmes two nodes met last. Chen et al. [3] consder not only that but also the frequency of nodes contactng the destnaton n the past and calculate the average. There are also some varatons of these algorthms. For example, Spyropoulos et al. [22] record the tme elapsed snce every other node was last encountered as the elapsed tme contans the relatve locaton nformaton of the nodes. And Chen et al. [4] develop an extended nformaton model to capture more hstory nformaton and use regresson methods to predct nodes future meetng probablty to gude routng. C. Socal-based Approaches As socal network applcatons explode n recent years, analyss of these network graphs shows that some nodes are the common acquantances of other nodes and act as communcaton hubs [15], [24]. Therefore, one promsng way of predctng future contact probablty s to use metrcs such as centralty and smlarty n network analyss to assess the message delvery probablty of a node based on the connectons n the graphs [5], [1], [18]. Nevertheless, n these network graphs, past node contacts have been aggregated nto a statc socal graph. As ponted out by [9], [27], the statc socal graph has the tradeoff between tme-related nformaton lost and predctve capablty. Some other MSN routng algorthms use socal features n user profles to gude routng. Me et al. [14] fnd that ndvduals wth smlar socal features tend to meet more often n MSNs. The ndvduals are characterzed by hgh dmensonal feature profles, though usually only a small subset of mportant features are extracted and used n routng. Wu et al. [26] provde a systematc multcast routng approach to resolvng socal feature dfferences between a source and destnatons by takng advantage of the structural property of hypercubes. The advantage of these socal-profle-based approaches s that they do not need to record node contact hstory. They work well n socal networks where the actvtes of ndvduals follow the nformaton n ther profles. In our recent work [19], we make our frst attempt to desgn routng algorthms for the IMSNs we address n ths paper. We fnd that n many moble socal networks, user actvtes are tme-dependent and may devate from ther socal features n ther profles. For example, someone who puts New York as hs state n hs user profle may actually attend a conference n Texas. Therefore, n order to capture nodes dynamc behavor to steer the routng n the rght drecton, we use dynamc socal features whch not only record a node s socal features but also ts meetng frequences wth other nodes havng the consdered socal features. Wth the smlarty metrcs derved from data mnng [8], we put forward a routng algorthm called [19] whch makes routng decsons based on the smlarty of nodes dynamc socal features. D. Hybrd Approaches In the lterature, there are also some hybrd approaches that consder more than one factor to make routng decsons. Sm- Bet [5] routng algorthm uses a hybrd forwardng rule that makes effectve use of two metrcs (centralty and smlarty) to determne the brdge nodes and nodes socal smlarty to the destnaton to delver data from one node to another. The centralty here refers to the betweenness centralty of each node, whch s estmated only n ts local neghborhood to avod exchangng the network topology nformaton. For the smlarty metrc, the number of common neghbors of the current node wth the destnaton s calculated. The Bubble rap algorthm [1] consders two characterstcs of a node- ts communty and centralty to make routng decsons. Here, a node can be a member of more than one communty and t has a local centralty showng ts popularty n ts own communty and a global centralty showng the popularty of the node n the network. Both the SmBet and the Bubble rap algorthms apply complex network analyss methods to socal network graphs bult by aggregatng past node contacts. III. OUR ROUTING ALGORITHMS In ths secton, we propose two hybrd routng algorthms and that select the next best forwarder based on ts hghest probablty to meet the destnaton resulted from the predctors usng node contact hstory and dynamc socal features as the current nformaton. Though these two algorthms use dfferent predctors, they use the same routng algorthm framework whch s presented n the next paragraph. A. Routng Framework of Our Algorthms Our algorthms and Enhance use the same routng framework as shown n Fg. 1 to delver messages from a source to a destnaton. The dfference between them s that they use a dfferent predctor r u d to make routng decsons. In the routng framework, we adopt delegaton forwardng [7], whch s proved by the authors to brng down the expected cost of message delvery from O(N) to O( N), where N s the number of nodes n the network. In delegaton forwardng, each node u s assgned a qualty r ud whch n our algorthms ndcates u s probablty to meet destnaton d n the future based on node contact hstory and dynamc socal features, and a level value τ. Intally, the level of each node s equal to ts qualty. In each hop of delegaton forwardng, a message holder u only consders forwardng the message to a node u j whch has a hgher qualty than u s level hopng that u j has a better chance to delver the message to the destnaton. At the same tme, node u mproves ts level to the qualty of u j. In the rest of the routng process, each message holder does the same thng untl the destnaton receves the message. The essence of delegaton forwardng s that a copy s transferred

4 Routng Algorthm Framework based on Node Contact and Dynamc Socal Features 1: Let u 1, u 2,, u N 1 be nodes n the network, d be the destnaton, and r ud be the probablty that node u wll meet d n the future based on node contact hstory and dynamc socal features. The calculatons of r ud n and are explaned n Sectons III-B and III-C. 2: Each node u has qualty r u d and level τ. 3: INITIALIZE : τ r ud 4: On contact between message holder u and node u j : 5: f u j s the destnaton d then 6: u forwards the message to u j and the algorthm s termnated 7: else f τ < r uj d then 8: τ r ujd 9: f u j does not have the message then 1: u forwards the message to u j 11: end f 12: end f Fg. 1. The routng algorthm framework to a newly encountered node f the node s closer to the destnaton based on a certan predctor than other nodes that the current node has already met. B. The Algorthm The predctor r ud of the algorthm s shown n Formula (1). It predcts the probablty of u meetng destnaton d usng a weghted combnaton of the hstory predctor h ud based on node contact hstory and the socal predctor s ud based on the smlarty of nodes dynamc socal features. The detaled calculatons of h ud and s ud wll be explaned n Sectons IV-A and IV-B, respectvely. In the formula, parameters α and β are weghts and α + β = 1. Note that when α s 1, the algorthm becomes the pure hstory-based algorthm and when β s 1, t becomes the pure dynamcsocal-feature-based algorthm. The ntuton of ths formula s that f u often met d drectly n hstory and/or t s very socally smlar to d based on the dynamc socal features, then t wll very lkely meet d agan n the future. r ud = α hstory predctor + β socal predctor = α h ud + β s ud (1) C. The Algorthm In the predctor r ud shown n Formula (2) for the, the socal predctor s enhanced by consderng not only the socal smlarty between u and d but also coverng a broader scope - the socal closeness between u and d s socal crcle. A node s socal crcle means a group of nodes that are socally smlar to the node. Here, specfcally, socal smlarty refers to the smlarty of nodes based on ther dynamc socal features. The ntuton of ths dea s that f u s socally smlar to d or often meets a set of nodes that are socally smlar to d, node u wll have a hgher probablty to successfully forward the message to d by tself or through one of the nodes n d s socal crcle. In Formula (2), parameters α and β are weghts and α + β = 1. Set L u contans the top L nodes that are socally smlar to d and frequently meet u, and s zd s the socal smlarty between a node z L u and d. Agan, how to calculate h ud and s zd wll be explaned n Sectons IV-A and IV-B, respectvely. r ud = α hstory predctor + β socal predctor z L = α h ud + β u s zd h uz (2) z L u h uz The becomes when we only consder the socal smlarty of u to d. In other words, when L u only contans u. IV. PREDICTOR CALCULATION In ths secton, we explan the calculatons of the hstory and socal predctors. We normalze each predctor to the range of [, 1] so that they can be of smlar order of magntude - otherwse they may overshadow each other when combned. A. Predctor For the hstory predctor, n [4], we proposed an nformaton model to capture more contact nformaton of nodes n hstory and used lnear regresson to predct future contacts for routng algorthms n DTNs. Snce t can catch more hstory nformaton and make good predctons [4], we adopt t to calculate the hstory predctor for routng algorthms n IMSNs as well. Its dea s as follows: We observe the past t tme ntervals {1, 2,, t} n hstory. Each tme nterval has a length of l unts. Let n (n l) be the number of contacts between node u and destnaton d n tme nterval. Let X- axs represent the tme nterval and Y -axs represent the number of contacts n. For t ntervals, we can obtan t ponts (, n ) (1 t) n the 2-D space as shown n Fg. 2. Although these t ponts (, n ) may not all le on a lne, t s reasonable to examne d = n (a+b) = n a b, whch s the dfference between the y-coordnates of the pont (, n ) and the correspondng pont on the lne y = ax + b. The Least-Squares-Method crteron for the best lnear model approxmaton s to determne the values of a and b that mnmze the sum of squares of all of the y-dfferences denoted by F (a, b) as follows: t F (a, b) = (n a b) 2. To mnmze F (a, b), we take the partal dervatves of F (a, b) and set them equal to to fnd the unque crtcal pont for F (a, b). F a(a, b) = t 2(n a b) =, F b (a, b) = t 2(n a b) =. Thus [ a b and ] = [ t 2 t t t ] 1 [ t n t n ]

5 Number of contacts n y d 1 1 d2 d3 d4 d5 d 6 d7 y = ax + b Tme nterval Fg. 2. Node contacts n the past tme ntervals [ ] a n t+1 = a(t + 1) + b = [ t ] b [ t t = [ t ] 2 ] 1 [ t t t n ] t n t t [ t ] t t = n t t 2 n t t ( 2 t )2. The value of n t+1 s the predcted future contacts of u and d n tme nterval + 1 based on ther contacts n the past t ntervals. We set h ud = n t+1 lt after normalzaton as our hstory predctor to estmate ther future meetng probablty. B. Socal Predctor For the socal predctor, the key ponts are how to represent nodes dynamc socal features and how to measure the socal smlarty of two nodes based on them. We explan them as follows. Suppose we consder m socal features F 1, F 2,, F m of nodes n IMSNs. We assocate each node wth a vector of ts socal features. For convenence, we use a node s label as ts vector s label. Thus, a node x has a vector x of x 1, x 2,, x m and a node y has a vector y of y 1, y 2,, y m. A node x s dynamc socal features are contaned n ts vector, whch s < x 1, x 2,, x m >= M1 M M total, 2 M total, M 3 M M total, m M total, where M s the number of meetngs of node x wth nodes whose value f of feature F s the same as that of destnaton d, and M total s the total number of meetngs of node x wth any other node n the hstory we observe. Thus x 1 for all 1 m. Wth the node s dynamc socal features defned, we can use the followng smlarty metrcs derved from data mnng [8] to compare the smlarty s xy of nodes x and y. Tanmoto smlarty It measures the smlarty of x and y as: s xy = x y. The notaton x y s the product x x + y y x y of the two vectors. For example, suppose we consder three socal features: Cty, Language, P oston. If the values of the socal features of destnaton d are: N ewy ork, Englsh, Student and node x has met people from New York 7% of the tme, people that speak Englsh 93% of the tme, and students 41% of the tme n the hstory we observe, then node x has a vector of x =.7,.93,.41. If y s vector s: y =.23,.81,.5, then usng the Tanmoto metrc, s xy =.82. x Cosne smlarty It measures the smlarty of x and y as: s xy = x y (x x)(y y). Eucldean smlarty After normalzng the orgnal Eucldean smlarty to the range of [, 1] and subtract t from 1, t s now defned m as s xy = 1 (y x ) 2. m Weghted Eucldean smlarty In addton to the basc Eucldean smlarty mentoned above, we also employ the weghted Eucldean smlarty to favor the socal features that are more nfluental to the delvery of the packet. To determne the weght of a socal feature, we use the Shannon entropy [21] whch quantfes the expected value of the nformaton contaned n the feature [26]. The Shannon entropy for a gven socal feature s calculated as: w = p(f ) log 2 (f k ), where w s the Shannon entropy for feature F, vector f 1, f 2, f k contans the possble values of feature F, and p denotes the probablty mass functon of F. The weghted Eucldean smlarty normalzed to the range of m [, 1] s: s xy = 1 w (y x ) 2 m w. V. SIMULATIONS Ths secton descrbes the smulatons we conducted usng a custom smulator wrtten n Java. We frst performed smulatons to determne the values of the parameters n our algorthms and then we compared our algorthms wth the exstng ones n two versons: sngle-copy and mult-copy. In our smulatons, we used the INFOCOM 26 trace [2], whch recorded conference attenders encounter hstory usng Bluetooth small devces (Motes) for three days at the IEEE INFOCOM 26 conference n Mam. Ths data set conssts of two parts: contacts between the Mote devces that were carred by partcpants and the self-reported socal features of the partcpants, whch are collected usng a questonnare form. The sx socal features extracted from the dataset and used for the socal predctor were Afflaton, Cty, Natonalty, Language, Country, and Poston. We use delvery rato, delvery latency, and number of forwardngs as mportant metrcs to evaluate the performance of the algorthms. An effcent routng entals a hgh delvery rato and low latency wth an acceptable number of forwardngs. A. Comparson of socal smlarty metrcs To fnd the best ft for our smulated context, we compared Tanmoto, Cosne, Eucldean, and Weghted Eucldean socal smlarty metrcs by performng delegaton forwardng routng algorthm. We utlzed the frst two days of the data as the ntal hstory and performed our smulatons on the remanng one day. We generated messages from a randomly chosen

6 Delvery rato Tanmoto Cosne.1 Eucldean Weghted Eucldean Tme (Seconds) Tanmoto 5 Cosne Eucldean Weghted Eucldean Tme (Seconds) Tanmoto Cosne.5 Eucldean Weghted Eucldean Tme (Seconds) (c) Fg. 3. Comparson of Tanmoto, Cosne, Eucldean, and Weghted Eucldean socal smlarty metrcs source to a randomly chosen destnaton every two seconds n the frst 24 hours of the smulaton. We then averaged fve separate smulatons for each smlarty metrc wth dentcal setups to mtgate the effect of any outlers n the performance. We set tme-to-lve of all of the packets to 9, meanng that a gven packet can be transferred at most nne tmes so that the delvery rato wll not always be 1% durng the whole tme frame of the trace. Results n Fg. 3 show that all of the metrcs performed smlarly n delvery rato, latency, and forwardngs. We therefore decded to use the Eucldean metrc snce t dd not requre the calculaton of addtonal weghtng values and performed slghtly better than Tanmoto and Cosne n latency. B. Determne α and β values To gve reasonable weghts for the hstory and socal predctors n our algorthms, we need to fnd out the values for α and β dependng on the trace we use. We tred < α, β > par to be: <, 1 >, <.25,.75 >, <.5,.5 >, <.75,.25 >, and < 1, > n and algorthms. The results of both algorthms showed that < α =.75, β =.25 > has the hghest delvery rato, comparatvely lower latency, and lower number of forwardngs. Therefore, we set α to.75 and β to.25 for our trace. The performance of usng dfferent α and β values s shown n Fg. 4. C. Determne the number of copes n mult-copy schemes We mplemented and n two versons: sngle-copy and mult-copy schemes. In the sngle-copy verson, only one copy of the message exsts n the network durng delvery. That s, each tme a message holder forwards the message to the next forwarder, t does not keep a copy for tself. In the mult-copy verson, we adopt the dea of bnary Spray-and-Focus [23] n DTN as the authors showed that bnary Spray mnmzes the tme to spray the message to newly encountered nodes and Focus can actvely delver the message to the destnaton. In the mult-copy verson of our algorthms, the source of a message ntally starts wth C(C 1) copes. Then routng s carred out n the Spray and Focus phases. In the Spray phase, any node wth c > 1 copes wll forward half ( c/2 ) of the copes to the encountered node wth no copy. Then n the Focus phase, f the destnaton s not found n the Spray phase, each message holder forwards the copy to the best encountered node selected by or. To determne the value for C, we tred multcopy versons of and wth C settng to 4, 8, 31, and 64. The smulaton results usng dfferent C values of both algorthms are consstent. As shown by the mult-copy verson of n Fg. 5, wth the ncrease of the number of copes, the delvery rato mproves, but the latency and forwardngs also ncrease. To reduce the cost, we therefore decded to set C to 4. D. Comparson wth exstng algorthms To evaluate the performance of our algorthms consderng both hstory and socal predctors, smulatons were conducted to compare them wth the exstng socal-analyss-based and socal-profle-based algorthms, and pure hstory-based and pure dynamc-socal-feature-based algorthms. The and algorthms were ncluded as benchmarks. The followng s the lst of algorthms we compare. To ft the legend n each fgure later, we create a short name for each algorthm. 1) The algorthm () [25]: Every message s spread epdemcally throughout the network untl t reaches ts destnaton. 2) The algorthm () [12]: The source holds the message untl t meets the destnaton. 3) The Socal-profle-based algorthm () [26]: It takes the dea from [26] where routng s guded by resolvng socal feature dfferences between source and destnaton usng socal features n user profles. 4) The Socal-analyss-based algorthm () [5]: Ths algorthm takes the dea from [5] where routng decsons are made usng socal analyss methods on the socal network graphs reflectng past node encounters. 5) The -based algorthm () [4]: It just consders the hstory predctor usng lnear regresson. 6) The Dynamc-socal-feature-based algorthm () [19]: It just consders the socal predctor usng dynamc socal features. 7) The algorthm (): Both the hstory and socal predctors are consdered wth weghts. 8) The algorthm ( ): Both the hstory and socal predctors are consdered wth the enhanced socal predctor. In the algorthms that nvolve socal features, namely,, and, the actual number of Motes used

7 8 6 8 Delvery rato (%) α=, β=1 5 α=.25, β=.75 α=.5, β=.5 45 α=.75, β=.25 4 α=1, β= α=, β=1 α=.25, β=.75 α=.5, β=.5 α=.75, β=.25 α=1, β= α=, β=1 2 α=.25, β=.75 α=.5, β=.5 1 α=.75, β=.25 α=1, β= (c) Fg. 4. The performance of sngle-copy usng dfferent α and β values Delvery rato (%) Copes=4 6 Copes=8 Copes=31 Copes= Copes=4 2 Copes=8 Copes=31 Copes= Copes=4 Copes=8 5 Copes=31 Copes=62 (c) Fg. 5. The performance of mult-copy usng dfferent number of copes was 62 n the trace after excludng 17 Motes that have no or partal socal features. We defne 1 tme nterval () as 1/1 of the whole trace tme length. Then 1 s s the tme length of the whole trace. In the and algorthms, we set α and β to.75 and.25, respectvely accordng to our smulaton results above. In the algorthm, the sze of L u s decded by h uz. We only select those nodes whose h uz >. The total number of these nodes does not exceed 1 n ths trace. For the mult-copy versons, we set C to 4 from the above dscusson. All of the comparng algorthms have a mult-copy verson usng bnary Spray-and-Focus. But and are a lttle dfferent n mplementaton. In, after the message s bnarysprayed to newly encountered nodes, the message holders stll delver the message epdemcally to the destnaton wthout beng constraned by the number of copes n the network. And n, the source holds the ntal copes of the message untl t meets the destnaton. We generated 5 packets between randomly chosen source-destnaton pars and appled them to all of the algorthms. The three performance metrcs, namely delvery rato, latency, and number of forwardngs, were calculated and averaged. The smulaton results of all of the algorthms n both snglecopy and mult-copy versons are consstent as shown n Fgs. 6 and 7. As expected, has the hghest delvery rato and lowest delvery latency but hghest number of forwardngs. has the lowest number of forwardngs but lowest delvery rato and hghest delvery latency. The pure hstory-based algorthm and pure dynamc-socal-feature-based algorthm outperform and n delvery rato and latency at the cost of the slght ncrease n forwardngs. That means, n our applcaton scenaro, the statc socal features n user profles and the lnks n the socal network graphs are less capable of capturng conference attenders actvtes to make good predctons. The tme-related predctors are better. The slght ncrease n the number of forwardngs shows that and are more actvely forwardng messages than and. Furthermore, our hybrd algorthms and are better n delvery rato and latency than the pure ones wth a slght ncrease n the number of forwardngs. Ths shows that the combnaton of the two tme-related predctors works better. From the ncrease n forwardngs, we can agan conclude that and are more actve n message delvery. Comparng wth, performs better n delvery rato and latency wth a few more forwardngs. Ths testfes our dea that consderng a node s socal crcle can facltate routng. VI. CONCLUSION In ths paper, we proposed novel hybrd routng algorthms for IMSNs where node connectons are tme-dependent and short-term by consderng two tme-related factors: node contact hstory and dynamc socal features to capture node moblty n IMSNs. We frst put forward a hybrd algorthm that makes a weghted combnaton of the hstory and the socal predctors based on these two factors. And then we upgraded t to by ntroducng a novel concept called socal crcle n the socal predctor to mprove message delvery. Smulatons were conducted to compare our algorthms wth the exstng socal-analyss-based and socalprofle-based algorthms, and wth the algorthms that only

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