On Modeling Software Architecture Recovery as Graph Matching

Transcription

1 O Modelig Software Architecture Recovery as Graph Matchig Kamra Sartipi Kostas Kotogiais Uiversity of Waterloo School of Computer Sciece ad, Dept. of Electrical & Computer Egieerig Waterloo, ON. NL 3G, Caada ksartipi, Abstract This paper presets a graph matchig model for the software architecture recovery problem. Because of their expressiveess, the graphs have bee widely used for represetig both the software system ad its high-level view, kow as the coceptual architecture. Modelig the recovery process as graph matchig is a attempt to idetify a sub-optimal trasformatio from a patter graph, represetig the high-level view of the system, oto a subgraph of the software system graph. A successful match yields a restructured system that coforms with the give patter graph. A failed match idicates the poits where the system violates specific costraits. The patter graph geeratio ad the icremetality of the recovery process are the importat issues to be addressed. The approach is evaluated through case studies usig a prototype toolkit that implemets the proposed iteractive recovery eviromet. Itroductio Most approaches to software architecture recovery view the recovery process as: i) a patter matchig problem that models the recovery by idetifyig groups of system etities whose properties closely match with the user-defied queries [0, 6]; ii) a clusterig problem that models the recovery by groupig the related parts of a software system ito cohesive compoets [8, ]; iii) a costrait satisfactio problem that models the recovery by idetifyig groups of etities that meet the coditios defied i a repository of plas [6]; iv) a lattice partitioig problem that models the recovery by classifyig maximally related groups of This work was fuded by IBM Caada Ltd. Laboratory - Ceter for AdvacedStudies (Toroto) ad the Natioal Research Coucil of Caada. etities that are arraged i a lattice []; or v) a compositio ad visualizatio problem that models the recovery by aggregatig system etities ito cotaimet-hierarchy of compoets [4]. The reverse egieerig commuity has also paid particular attetio to the patter matchig approaches sice they allow the use of domai kowledge ad system documetatio i composig the patter, hece provide a user/tool cooperative eviromet for architectural recovery. Moreover, the software systems are ituitively represeted as graphs ad the reverse egieerig commuity is o the verge of adoptig a graph stadard for iformatio exchage amog the existig reverse egieerig tools []. This paper presets a approach to software architecture recovery that cosiders the high-level desig of a system as a patter graph, ad models the recovery process as a graph patter matchig problem that matches such a highlevel patter graph of the system with a etity-relatioship graph represetatio of the source-code system etities. The motivatio for this research stems from the lack of a reflective ad uiform model for patter-based software architectural recovery, whereby the software system, architectural patter, ad patter matchig process, are all uiformly represeted usig a graph formalism, ad the recovered architecture coforms with detailed costraits of the architectural patter. The remaiig sectios of this paper are orgaized as follows. The related work is discussed i Sectio. Sectio 3 presets the proposed eviromet for architectural recovery. Sectios 4 ad represet the software system ad its architectural patter. Sectios 6 ad discuss the graph matchig process ad modelig. Sectio 8 presets the tractability of the matchig process. Sectio provides the steps for patter geeratio, ad Sectio 0 presets the architectural recovery case studies.

2 Off lie O lie pre process aalysis Software System C / Pascal /... System aalysis Domai & Documet Decisio makig Module Itercoectio patter AQL query RSF Parsig AST Query geeratio User assisted Data miig Software as graph Architecture & Metrics Graph geeratio Automatic Software graph regios & Similarity matrix Graph matchig egie (search & evaluatio) Patter graph Figure. The iteractive eviromet for the proposed patter-based software architecture recovery. Related work The related approaches to this work iclude the followigs. I Dali [] a patter cosists of a collectio of SQL queries that collect the architectural compoets ad their derived relatios, whereas the approach i this paper presets a modular patter of the software system usig the AQL queries. I [6], the user defies a architectural patter or style as a graph of compoets ad coectors represetig sigle elemets ad uses approximate matchig to idetify the patter i the software system. I cotrast our approach defies a macroscopic patter o the groups of system etities ad the iteractio amog the groups of etities. I [0], a software reflexio model is proposed to assist the user i testig his/her metal model of the system usig textual declarative forms. I cotrast, our approach uses a structured query as patter ad architectural costraits to be satisfied i the recovered architecture, as opposed to checkig the validatio of the facts i the patter. The approach i this paper also relates to our previous work o a graph patter matchig approach to software architecture recovery [4]. Specifically, the cotributios of this paper iclude: i) providig represetatio models for the software system beig aalyzed ad the high-level patter of compoets ad costraits; ii) modelig the graph matchig process by a set of recursive graph equatios; ad iii) steps for geeratig the architectural patter graph. 3 Proposed eviromet for recovery process Despite several attempts for automatig the architectural recovery process (i.e., clusterig) it is geerally accepted that a fully-automated techique is ot feasible. It is rather difficult to extract the architecture of a large system at oce, hece, the architectural recovery should be a icremetal process. Software systems usually cosist of patters i their desig which form the basis for the recovery process. Most recovery processes focus o the structural properties of a system, igorig the high-level behavior of the system. Fially, the role of the user is icreasigly importat i icorporatig the domai kowledge ad system documets ito the recovery process. Based o the above discussio, this paper defies the software architectural recovery problem as: devisig a tractable methodology ad the supportig tools for iteractively ad icremetally extractig a system s structure usig domai ad system kowledge. We propose a iteractive reverse egieerig eviromet for icremetal recovery ad evaluatio of the architecture of a software system i the form of cohesive modules (or subsystems) that comply with the costraits of a user-defied patter. Figure illustrates the differet parts of the proposed iteractive architectural recovery eviromet where the thick arrows sigify the automatic or user-assisted processes i the eviromet; boxes represet the differet forms of iformatio i the eviromet; the thi arrows idicate the iputs ad output of the graph matchig egie; ad the user is the high-level decisio maker that produces a metal model of the architecture ad verifies the result of recovery. The eviromet cosists of a off-lie pre-process phase ad a o-lie aalysis phase. Durig the off-lie iformatio extractio phase, the software system, writte i a procedural laguage such as C, is parsed ad preseted as a attributed relatioal graph

3 whose odes ad edges coform with a domai model that is suitable for architectural recovery. Such a domai model provides programmig laguage idepedece for the recovery process. The graph represetatio of the software system is further processed ad is divided ito a collectio of subgraphs, where the appropriate subgraphs are selected by the graph matchig process as the subspaces for recovery of the system compoets. Also, a similarity matrix is geerated that cotais the associatio-based similarity values betwee every two system etities to be used for recovery of cohesive compoets. Durig the o-lie aalysis phase, the user defies a graph-based architectural patter of the system modules (subsystems) ad their iteractios based o: domai kowledge, system documets, or tool-provided system aalysis iformatio. I a iterative recovery process, the user costraits the architectural patter ad the tool provides a decompositio of the system etities ito modules or subsystems that satisfy the costraits. I this approach, the architectural patter is viewed as a graph of modules (or subsystems) ad itercoectios, where each module (oe ode of graph) represets a group of placeholders for the system etities (i.e., fuctios, types, variables) to be istatiated, ad each budle of itercoectios (oe edge of graph) betwee two modules represets data-/cotroldepedecies betwee two groups of placeholders i two modules. The miimum/maximum sizes ad the types of both placeholders ad the itercoectios are cosidered as free parameters to be decided by the user (respectig the allowed relatio betwee two etities). This yet u-istatiated module-itercoectio represetatio (ca be referred to as coceptual architecture) is directly defied for the tool, usig a proprietary laguage that we call Architecture Query Laguage (AQL) ad is discussed i [4]. Patter-graph: the AQL query is icremetally expaded to geerate a patter-graph that represets a macroscopic view ad structural costraits for a part or the whole of the system architecture to be recovered. The task of the tool is the to search through the software system (agai represeted as a graph of system etities ad relatioships) to fid a sub-optimal match betwee the patter-graph ad the graph of the system. The architectural recovery is performed at two levels of abstractio. At the file-level, the software system is decomposed ito a umber of subsystems of files, ad at the fuctio-level each recovered subsystem ca be decomposed ito a umber of modules of fuctios, datatypes, ad variables. 4 Software system represetatio I this approach the software system ad the architectural patter are preseted usig the attributed relatioal graph otio defied i [3]. Source-graph: the software system is represeted by the source-graph, where the odes ( ) represet files, fuctios, datatypes, ad variables ad the edges ( ) represet cotai ad use relatioships. The odes ad edges comply with the specific domai model, amely abstract domai model, illustrated i Figure (b). I this model differet types of etities, i.e., File-abs, Fuctioabs, Type-abs, Variable-abs, are a subset of the types of etities i the software system s source-code. Where, Fuctio-abs deotes fuctios, Type-abs deotes aggregate/array types, ad Variable-abs deotes global variables i the software system. Also, fuctios, datatypes, ad variables are called simple etities, ad files are called composite etities such that a file may cotai zero or more simple etities. Each relatio i the abstract domai model, i.e., use- F, use-t, use-v, cot-r, use-r, imp-r, exp-r, is a aggregatio of oe or more relatios i the software system s source-code. The relatios use-f, use-t, use-v are defied such that the implemetatio of a fuctio-abstractio (i.e., a fuctio i the source-code) calls aother fuctio; updates/reads a variable whose type is a aggregate/array type; or updates/reads a global variable, respectively. The relatio cot-r (i.e., cotaied resource) is defied such that, each simple etity ca be cotaied i oly oe file; the simple etities i the library files are cotaied i the file abstractios based o the maximum frequecy of usig the simple etities by the files. I this cotext, the exterally defied library files ad their cotaied simple etities are ot cosidered. The relatio use-r (i.e., use resource) is defied such that a file cotais a fuctio ad that fuctio uses a simple etity as described above. The relatio imp-r (i.e., import resource) is defied such that a simple etity is cotaied i aother file but is used by the subject file (ad vice versa for exp-r). Based o the above abstract domai model the software system is parsed ad represeted as a attribute relatioal graph whose abstractio-level is suitable for architectural aalysis, as it is illustrated i Figure (c). Two labelig fuctios ad i Figure (c) are used to retur the importat attribute values of the odes ad edges of the source-graph i the form of a list of attribute, attributevalue pairs. I Figure (b), the class Etity-abs (Relatio-abs) presets the commo attributes that are iherited by every etity (relatio) i the abstract domai model. These attributes idetify a source-code costruct (e.g., defiitio, declaratio, statemet, fuctio-call, assigmet) that implemet a specific etity or relatio. Each relatio i the abstract domai model is a object of a associatio class ad cotais the attributes from ad to deotig the source ad destiatio etity for that relatio.

4 Comp placeholders groupid: $ CL / CF / CT / CV micot: Iteger maxcot: Iteger etities: set (Etity abs) imports: set (Co placeholders) exports: set (Co placeholders) 3 etity: Etity abs type: Relatio abs idex: Iteger from: Compoet to: Compoet.. Co etity Co placeholders groupid:? R / F / T / V Iteger type: Relatio abs mietities: Iteger maxetities: Iteger etities: set (Co etity) from: Compoet to: Compoet AQL query text Module M Module M. Module M4 Subsystem ame: Strig maiseeds: set (Etity abs) part: Comp placehoders High level view Low level view Compoet AQL query ame: Strig cotais: seq (Compoet) Module ame: Strig maiseeds: set (Etity abs) parts: seq (Comp placehoders) Etity abs Relatio abs Abstract domai model (a) Architectural domai model Mai seed Fuctio abs?f(..) Parse Query graph F: (..4) M?V(0..4)?F(..6)?F3(4..8) M M4?T(..4) F: (4..6) F: (..8) Graph matchig Architectrual domai model F: (..3) M3?T(..3) Etity abs ame: Strig file #: Iteger lie #: Iteger implemet id: Char Iteger s ( ) = ((type, Fuctio abs), (ame, "/u/../foo"), (id, F6), (lie#, 3), (file#, )) µ 4 3 SimpEt abs ε s (r 8) = ((from, ), (to, 8), (type, use F), (lie#, ), (file#, )) File abs Variable abs Type abs Fuctio abs id: L Iteger id: V Iteger id: T Iteger id: F Iteger imports: set (SimpEt abs) usefucs: set (Fuctio abs) exports: set (SimpEt abs) usetypes: set (Type abs) cotais: set (SimpEt abs) usevars: set (Variable abs) uses: set (SimpEt abs) 3 8 Source graph Parse Abstract domai model cot R from: File abs to: SimpEt abs use R from: File abs to: SimpEt abs Aggregatio Geeralizatio imp R from: File abs to: SimpEt abs Associatio class exp R from: File abs to: SimpEt abs Relatio abs use V from: Fuctio abs to: Variable abs file #: Iteger lie #: Iteger implemet id: Char Iteger use T from: Fuctio abs to: Type abs use F from: Fuctio abs to: Fuctio abs (b) Abstract domai model Software system (c) Matchig the high level graph of the system with the source graph of the system Figure. Represetig the architectural patter ad the software system as two graphs usig the architectural domai model ad abstract domai model, respectively.

5 ! : N 0 : N Reducig the search space: the source-graph provides a search-space for the matchig process. However, sice eve i a medium-size software system the umber of etities ad relatioships that are geerated are prohibitively high, ay matchig algorithm will be itractable. Matchig phase: to address the tractability of the matchig process, the whole process is divided ito icremetal phases (as partial-matchigs) where is the umber of compoets to be recovered ad the curret matchig phase is idetified by ( [.. No. of compoets]). Therefore, the recovery process performs a multiphase matchig. Source-regio: the search space for the matchig process is divided ito a collectio of sub-spaces usig data miig associatio relatio defied i [4], where each sub-space is a subgraph of the source-graph, amely a source-regio. All the odes i a source-regio are associated with a distiguished ode i that regio which is called the mai-seed of the regio. The group of source-regios s i the source-graph are stored i a database ad at the matchig phase the user selects a source-regio from the database to be matched with the icremetal part of the patter. Therefore, the source-regio is show as where is a fuctio that maps the curret matchig phase (i.e., ) to the id-umber of the selected source-regio (i.e., ). At file-level aalysis the source-regio odes are files fuctios, datatypes, variables, ad at fuctio-level aalysis the source-regio odes are fuctios, datatypes, ad variables. Architectural patter represetatio The architectural patter is represeted by a AQL query that defies a macroscopic patter graph for the software system to be matched agaist the source-graph. Query-graph: the sytactic costructs of a AQL query coform with the architectural domai model of Figure (a) that defie a query-graph. I this domai model, a AQL query, or equivaletly a query-graph, cosists of a umber of abstract compoets. Each abstract compoet (or simply a compoet) ca be either a subsystem or a module. A abstract compoet is specified as a collectio of placeholders. The itercoectios amog the abstract compoets are established by the meas of abstract coectors, where a abstract coector is also specified by a umber of placeholders. A placeholder is a ode that ca be matched with a system etity i the abstract domai model durig the matchig process. The user ca costrai the miimum ad maximum umbers of the matched placeholders ad their types i the recovered compoets ad coectors by formulatig the AQL query. Each abstract compoet cotais oe or more fixed etities, amely mai-seed(s), that appear i the result of the recovery. The mai-seed(s) for a abstract compoet determie the source-regio(s) to be searched for recovery of that compoet. I Figure (c), a AQL query with four modules is parsed ad represeted as a query-graph with four odes that is iterpreted as follows. The module M with mai-seed ode will be matched with miimum 4 ad maximum 6 fuctios i the source-graph (preseted as : ), will import betwee $#%& to fuctios from module M (preseted as "! ), ad will export betwee ) to 4 datatypes to module M4 (preseted as '(! ). The iteractio of M with other modules is ot restricted. Patter graph geeratio: the query-graph ( is used to derive a patter-graph ad a iput-graph that are required for the icremetal graph matchig process. At matchig phase the query-graph icremetally geerates the patter-graph +* as follows. Patter-regio: the,$- ode of the query-graph (as the abstract-compoet. ) is expaded ito a patterregio /* through: i) geeratig the maximum umber of placeholder odes (or simply odes) defied by. ; ad ii) coectig every ode i the patter-regio to every other ode i the patter-regio that are allowed based o the types of the odes. Edge-budle: each edge "3 of the query-graph (, e.g., ad of type use-f is ex- edge with label (0 paded ito 43 0 umber of edge-budles of the same type. Each edge-budle coects every ode from a already recovered compoet to oe ode (i.e, the commo sik or source ode) i the patter-regio * with respect to the directio of the query-graph edge. Iitially, the first max odes of the patter-regio are selected as the commo sik/source odes of the idividual edge-budles. However durig the matchig process the commo sik/source ode of a edge-budle which is ot matched yet ca be redirected to aother ode of the patter-regio. Each edgebudle correspods to oe ode of the ivolvig compoets to be imported or exported. The group of edgebudles betwee the already recovered compoets (modules or subsystems) ad the curret patter-regio * is * ;: represeted by 68. The ratioale for geeratig the edge-budles is to al- A group of coector-edges is deoted by <=?>A@B=C ad represet a group of edges that coect two graphs DFE ad DHG. The coectoredges represet the iteractio betwee two graphs i ui-directioal (usig I or J ) or bidirectioal (usig K ) mode. The coector-edges betwee a matched-graph DMLNPO E (discussed later) ad the source-regio DRQS T;UN)V at phase W are deoted by < QS, ad the edge-budles betwee a matched-graph D LNO E ad the patter-regio DX S at phase W are deoted by < X S N.

6 AQL query Phase matched Phase beig matched Module M Module M 6 4 matched graph co edges 0 3 source regio (c) Iput graph 4 (d) Matched graph 6 3 F: (..4) M 6 Mai seed?f : (..) F:(..3) M (a) Represetig a AQL query as a Query graph. The Query graph geerates patter graph ad iput graph i parts (b) ad (c). m G m G matched graph m sr R ( m R ( pr edge budle + + sr G g() pr G patter regio, I G p G Match 4 (b) Patter graph, ) ) = =,3 matched graph m G = G m m mr + ( R + +, co edges + Graph summatios Mai seed matched regio G mr ) Source graph edge U matched edge Figure 3. The graph patter matchig process iteratively matches a patter-graph with a iput-graph ad yields a matched-graph as the recovered architecture for the curret matchig phase. low every subset of the odes i a source compoet to be coected to every subset of the odes i the destiatio compoet, accordig to the costraits defied i the query-graph. Figure 3(a) illustrates a query-graph with two odes that represet two abstract-compoets M ad M as modules, ad a edge that represets a abstract-coector?f:(..). This query-graph has the required iformatio to geerate the icremetal parts of both the patter-graph * ad iput-graph at phase of the matchig process. The ode M with ode costrait F:(..3) geerates a patterregio /* with maximum of three placeholder-odes ( to ) of types Fuctio-abs ad the edge?f:(..) geerates two edge-budles represeted by 6 C i Fig- * ure 3(b). Also, the ode M idetifies the selected sourceregio with mai-seed ode i Figure 3(c), correspodig to. 6 Graph matchig process A patter-graph +* by its defiitio is composed of a umber /* of smaller patters (i.e., idividual patter-regios at differet matchig phases ). This compositio property allows to maage the complexity of the matchig process of a large source-graph by applyig it o a regio-byregio basis. Matched-graph: at matchig phase, the matchig process computes a sub-optimal match, amely the matchedgraph betwee a patter-graph +* that origiates from a query-graph ad a iput-graph that origiates C from the from the source-graph. The obtaied result must coform with the costraits of the query-graph with respect to the ode ad edge size-rages. I Figures 3(b),(c),(d) a example of matchig process at phase is illustrated, where the patter-regio +* * ad its edge-budles 6 C from the patter-graph * are matched agaist the sourceregio ad its coector-edges 6 C from the iput-graph. The result of matchig is the matchedregio ad its coector-edges 6 matched-graph. At the ext iteratio, the matchedgraph is used to build the patter-graph * ad iputgraph to be matched at phase 3 (ot applicable i this example). Graph model of the matchig process The graph summatio otatios plus for coectig two graphs, ad oplus for coectig a graph to a group of coector-edges are used to model the whole icremetal patter matchig process i terms of the recursive graph algebraic equatios. Figure 4 illustrates the proposed graph matchig model where is the matchig phase ad is the umber of odes i the query-graph (. I this cotext, the matched-graph at phase zero is defied as a graph with zero umber of odes ad edges, ad whe the /* *,, ad the matchig process termiates. The approximate matchig process (equatio 4) aims to compute a match betwee the patter-graph +* ad the iput-graph by comparig differet subgraphs of the iput-graph agaist a

7 .!. : 6 /* * ;: /* 3. 6 "3 /* 4. +* /*. +*. : "!$# "!# "! &% ')(, ')(, % :+*,,0/ -!,- %43,.- : /* * Figure 4. The recursive equatios for the proposed multi-phase, icremetal, ad approximate graph matchig process. trasformed versio of the patter-graph *. A subgraph with miimum graph distace to the patter-graph * (a graph distace is computed as the total cost of a umber of trasformatios o the patter-graph * such as ode or edge deletio/isertio) is the solutio of the matchig process which is called the matched-graph.. Cost evaluatio for graph matchig The equatio i Figure 4 defies the distace betwee the patter-graph +* ad a subgraph of the iput-graph, as the sum of the graph trasformatio costs for matchig all the placeholder-odes iside the patter-regio +* with odes from the subgraph. I this distace, the costs for deletig the edges from iside the patter-regio ( 6!$# &% ), the cost for deletig the edges from the edge-budles ( 6!$# '(, ), ad the cost for isertig the coector-edges ( 6! '(, ) are computed. We ote that, oly the icremetal parts of the patter-graph * ad the iput-graph at matchig phase are beig matched ad the matched-graph at phase 8! is fixed, as show i Figure 3(b) ad (c). I the followig, these costs are defied. 6!$# Iside-edge deletio cost, &% : this cost is defied i Figure (a) with the objective of recoverig cohesive compoets as the matched-regios s at differet matchig phases. This cost has two sub-costs. The first sub-cost is deoted as the default dissimilarity value betwee the cadidate-ode ;: ad each matched ode i /* where is the similarity value betwee two odes accordig to a similarity metric such as the associatio similarity metric defied i [3]. The secod sub-cost =< # depeds o the umber of deleted edges betwee two odes. The coefficiet 0. idicates the sigificace of each missig edge compared to the dissimilarity value betwee two odes. Hece, each missig edge adds a value of =< to the default cost value, ad at worst case (two edges deletio) the dissimilarity # & value doubles. Therefore, icreasig the coefficiet > causes that the missig edge to become more importat tha the dissimilarity value, ad vice versa. The costs for differet cases of iside-edge deletio are show i Figure (a).?!# Coector-edge deletio cost, '(, : this cost is defied i Figure (b) based o the umber of remaiig edge-budles durig the matchig process at phase where the placeholder-ode is to be matched with cadidate-ode : from the selected source-regio P. At this time, the placeholder-odes i patter-regio +* ad their coector-edges (to previously matched-regios ) have already bee matched. Iitially, for each ode to be imported or exported betwee the ivolvig compoets oe edge-budle has bee geerated. As a example, for a abstract-coector with miimum cardiality ad maximal cardiality 3, three edge-budles are iitially geerated. Therefore, durig the matchig process, for each ode to be imported/exported oe edge-budle must be deleted. The umber of remaiig edge-budles idicates the umber of odes that ca still be imported/exported to reach to the maximum umber of allowed coector-edges. To perform cost evaluatio, the coector-edges are further classified ito two groups imported ad exported. Because of the space limitatio, we oly discuss the cost for imported coector-edge deletio i this paper. Imported coector-edge deletio: for importig each ode (which is equivalet to matchig a imported coector-edge whose source ode has ot bee imported earlier) a whole imported edge-budle must be deleted with o-cost. However, withi the edge-budle that is coected to the curret placeholder ode, for each edge deletio a cost is applied. The cost evaluatio steps alog with a example are illustrated i Figure (b). I this cost, is the umber of remaiig edge-budles icludig the curret edge-budle, i.e., is equal to the differece betwee maximum umber of allowed edges to be matched ad the umber of curretly matched edges. The value of this cost depeds o the success of the cadidate-ode : i augmetig the umber of matched imported edges to reach to its maximum umber. Therefore, matchig more imported edges by the curret ode meas less cost. This cost is calculated based o the eligibility of the ode to produce a cohesive module, by takig ito accout the iside-edge deletio cost "!$# &%. The coefficiet 0. has bee empirically determied to give more weight for collectig a group

8 d = 0 ed s 0. d s C = + k i m m d = d = = Maximum similarity betwee two etities i the curret source regio. s = similarity value betwee k ad x m = umber of already matched odes d = umber of deleted edges x ed C = i s ed 0. s ed 0. s C = C = m i m i m (a) Cost for iside edge deletio Cost evaluatio steps "r" = umber of remaiig edge budles icludig the curret edge budle Keep "r" edges from the curret edge budle (icludig edges that will be matched) ad delete the rest with cost "zero". 3 Match the edges from "r" edges i edge budle. 4 From "r" edges, each edge that is ot matched, is deleted with cost: x 0. x C ed r i Example: r = 3 ad edges are matched deleted: cost Curret ed edge budle x 0. C 3 i r matched edge matched edge deleted: cost zero matched ode deleted: cost zero = i,j k (c) to (e) Examples for part (b), 8,,... =, 8,,... (b) Cost for imported coector edge deletio mr G u bi bi i, pr G i i,3 (c) A portio of the patter graph p G i at phase i. 8 i, 8 first matched ode = 4 i, i, i,3 (d) Two edges matched from edge budle bi : i) edge budle bi is deleted with o cost; ii) third edge of bi is deleted with o cost. edge budle 8 = i, i, = 3 i,3 secod matched ode (e) Secod matched ode causes o edge match, (or the matched edges already imported): i) redirect edge budle to ext ode with cost. Figure. The cost evaluatio for deletig edges that are located: a) iside the patter-regio, ad b) withi the edge-budles betwee a recovered module ad the patter-regio. of related odes as opposed to satisfyig the max umber of imported coector-edges. However, this cost evaluatio is applied oly if the miimum (maximum) umber of imported coectoredges for patter-regio +* still ca be reached (ot exceeded) by the umber of matched coector-edges for the curret ode-matchig with :. Otherwise, the cost is maxcost ad this ode-matchig will be discarded. 6! Coector-edge isertio cost, ')(, : If there exist edge-budles betwee the patter-regio * ad the matched-regio ( (@ A ) i the patter-graph +* the the cost of isertig a coector-edge * : (i the same directio as the edge-budles) i 6 is maxcost. Otherwise the cost is zero, which meas the iserted coector-edge is ot part of the costraied itercoectio patter specified i the patter-graph, hece isertig oe or more ew coector-edges does ot violate the itercoectio patter. Figures (c) to (e) illustrate a example with two cases of matchig imported coector-edges where the maximum cardiality is. 8 BQ- search algorithm We use the search algorithm that is modified by a bouded path-queue heuristic to compute a sub-optimal matchig cost betwee the patter-graph * ad iputgraph while the AQL query costraits are ot violated. The search algorithm geerates a search-tree that correspods to the recovery of each abstract-compoet. i the query-graph (. At each ode of a search-tree the cost of graph trasformatios for matchig a ode : ad its edges from the source-regio with a placeholder-ode ad its edges from the patter-regio are evaluated ad the search-tree is expaded from a tree-ode that has the miimum cost. The cost evaluatio was discussed earlier.

9 Each search-tree has a maximal depth equal to the umber of placeholder-odes i the patter-regio (or equivaletly to the maximum umber of placeholders i the abstractcompoet. ). 8. Tractability of the matchig process The proposed eviromet for architectural recovery i Figure icorporates several techiques i order to tackle the iheret complexity of a architectural recovery processes ad to provide a tractable ad iteractive recovery process. These techiques are discussed below. Sub-optimality to achieve performace. A major drawback of the optimal search algorithms such as is the requiremet to maitai all icomplete tree-paths (partially-matched graphs) i a sorted queue that allows to select the cheapest tree-path to expad ext. This queue grows very fast ad i the worst case ca have a expoetial size, which makes the process of storig ad sortig the paths i the queue as a bottleeck for the algorithm. Sice the path queue is sorted, all of the eligible paths to be expaded (i.e., low cost paths) are located toward the head of the queue. Therefore, most of the paths with high cost at the ed of a large path-queue will ever get a chace to be expaded, ad remai at the tail of the path-queue util the ed of a successful search. This property allows us to restrict the size of the path queue withi a reasoable rage (e.g., multiple hudreds of paths) at the expese of obtaiig possibly a suboptimal solutio. We call this algorithm Bouded Queue (BQ- ). Search space reductio. The whole search process is divided ito a multi-phase search process, where at each phase the modified search (BQ- ) recovers a idividual module usig a reduced search space kow as a source-regio. Therefore, the whole search space, i.e., all odes of the source-graph with the cardiality is reduced ito odes, which greatly cotributes i relaxig the search complexity. Hierarchical architecture recovery. The proposed architectural eviromet i Figure allows to perform architectural recovery at two levels of graularity for the system etities, such that: i) at file-level a system of files is decomposed ito a umber of subsystems of files, ad ii) at fuctio-level each geerated subsystem ca be decomposed ito a umber of modules cosists of fuctios, datatypes, ad variables. Implemetatio cosideratios. The implemetatio of the coector-edges is crucial i reducig the complexity of the proposed matchig process. The mai ideas are as follows: i) prevetig highly repeated operatios o the source/sik odes of the coector-edges by cachig the source/sik odes; ii) simplifyig the edge-budle implemetatio by represetig it as a positive iteger. Therefore, deletig a whole edge-budle or matchig a part of edges i a edge-budle simply meas decremetig the iteger by oe; ad redirectig a edge-budle meas o chage o this value. Icremetal patter geeratio & recovery The architectural patter that is defied i the AQL query ad represeted by the query-graph ( is geerated through a icremetal ad iteractive process, as described i the followig steps. Step. Decide o a method of mai-seeds selectio for the AQL abstract modules/subsystems. The proposed methods iclude: i) utilize kowledge about the related domai such as a referece architecture with well-defied compoets, desig documetatio, iformal iformatio embedded i the source-code, amig covetios, or directory structures; ad ii) cosider system aalysis ad metrics such as associatio structure of the system files ad differet methods of clusterig []. The adopted method(s) should be able to suggest importat ad rather distict mai-seeds as the cores of fuctioality for the abstract module/subsystems i the AQL query. Geerate a AQL query with zero modules/subsystems. Step. Select the mai-seed for the ext module/subsystem ad assig the umber of placeholders, e.g., 0 for subsystem recovery ad 0 for module recovery. Recover the ew module/subsystem where o lik costraits are defied for the ew module/subsystem. Step 3. Ivestigate the quality of the ew recovered module/subsystem ad its iteractio with the already recovered modules/subsystems. If the recovery is satisfactory go to Step. Otherwise, defie (or adjust) the miimum/maximum lik costraits betwee the ew module/subsystem ad oe or more previous modules/subsystems, cosiderig: i) icreasig the maximum rage causes the matchig process to allocate higher scores to the group of etities that ca augmet the umber of iteractios to this maximum rage; ad ii) the miimum rage is used to restrict the umber of iteractio to a miimum threshold, however it does ot affect the scorig mechaism. The user s kowledge about the fuctioality of the modules/subsystems is required i order to impose meaigful costraits o the modules/subsystems iteractio.

10 mai-seeds u_elastic u_drag e_edit No. of Placeholders Recovered files + Distributed files Phs?R(0..0) S-S4?R(40..00)?R3(40..00) S?R4(0..0) 0 Phs Patter matchig files 8 fucs R(30) S-S4 R(00) R3(66) S R4(0) + 6 files 668 fucs 3 Phs S3 S 0 Phs e_scale f_readtif (a) Architectural patter usig AQL query 3 + files 3 fucs + files S3 S 4 fucs (b) Recovered architecture S- S4 S Recovered subsystems No. of files Xfig subsystems No. of files Precisio Recall editig & 63% S-S4 3 utility & 4 8% 4% drawig 00% u_drag u_elastic e_edit S S3 3 0 X-widowig editig & utility & 8 3 8% 6% 64% 3% 3% S 0 file maipulatio 6 0% 44% S3 S rest-of-sys 8 zero size files rest-of-system e_scale f_readtif Xfig subsystems: ) editig: files ) utility: 8 files 3) drawig: 0 files 4) file maipulatio: 6 files ) X-widowig: 8 files (c) Xfig recovered subsystems: liks are strog associatios amog files (d) Arcitectural recovery evalutio usig "Precisio" ad "Recall" Figure 6. (a) Architectural patter of the Xfig system where the subsystems S ad S4 have bee merged. (b) Recovered architecture where the lik costraits have bee satisfied. (c) Graph visualizatio of the recovered subsystems usig the file associatio graph. (d) Architectural evaluatio. Step 4. Repeat the recovery process for the ew module/subsystem with the costraied liks. If the process is very legthy due to backtrackig, the iterrupt the process ad observe the tool-provided ru-time iformatio about the critical costraied liks. Go to Step 3. Step. If the umber of the recovered modules/subsystems is ot sufficiet accordig to the user s prefereces go to Step. Otherwise stop the recovery process ad succeed. If the umber of remaiig etities i the rest-of-system is high, a extra step, amely costraied distributio ca be performed. I this step a part of the remaiig etities i the rest-of-system are allocated to the recovered modules/subsystems based o the highest average closeess of each etity to oe of the recovered modules/subsystems, provided that this allocatio does ot violate the lik costraits. If a lik costrait is violated the ext highest module/subsystem is tried util the allocatio to ay of them violates the lik costraits, where the etity is retured to the rest-of-system. 0 Case studies I this Sectio, the experimetal results by applyig the proposed approach are preseted. A comprehesive set of experimets related to the time/space complexity, accuracy, stability, ad quality of the architecture recovery techique has bee preseted i []. The proposed techique has bee implemeted i Alborz [], a prototype toolkit that aims to recover the architecture of the medium size systems implemeted i a procedural laguage such as C. The iput to the Alborz tool is a iformatio base that correspods to the etities ad relatioships of the software system i the form of a AST or RSF file. The tool provides the result of the architectural recovery ito two forms: i) HTML pages for the recovered compoets, tool geerated metrics, ad source code, to be visualized by a Web browser such as Netscape; ad ii) graphs of boxes ad arrows to be visualized by the Rigi tool [], where the boxes are the system files or the aalyzed compoets ad the arrows are either the resource iteractio (i.e., import/export) betwee the compoets or their associatio stregths. The associatio values amog the system files are distributed over a wide rage of values, hece they ca be classified ito several sub-rages, amely stregths of associatio cosist-

11 ig of four sub-rages of strog, medium, loose, ad weak. This classificatio of values allows to simplify the visualizatio of the associatio graph of the system files or compoets (i.e., modules or subsystems). The experimets are performed o six middle-size idustrial systems, amely: i) Xfig.3..3 drawig editor with 4 KLOC, ii) Clips.4.0 expert system builder with 40 KLOC, iii) Apache...4 http server with 38 KLOC; iv) Bash..03 Uix shell with 44 KLOC; v) Elm...6 Uix mail system with 3 KLOC; ad vi) Ghostview.3..8 postscript file viewer ad avigator with 3 KLOC. However, because of space limitatio oly oe case is preseted here. Architecture recovery of Xfig. The Xfig system [] lacks ay documetatio o its structure ad oly the user maual exists. However, a cosistet amig covetio is used throughout the system files which ca be used as a aid for iferrig its structure. Figure 6(a) illustrates the geerated architectural patter of the Xfig system with four abstract subsystems ad correspodig lik costraits accordig to the steps i Sectio. Durig the icremetal ad iterative recovery process this patter yields the recovered architecture i Figure 6(b) where the size costraits for both the subsystems ad liks have bee satisfied. Figure 6(c) illustrates the file associatio graph feature of the proposed eviromet for viewig the Xfig recovered architecture, where oly the strog ad medium associatio liks are show. The highly associated files are grouped ito subsystem S-S4 ad the associatio amog the subsystems are limited. The subsystem S-S4 has high associatio with subsystem S3 but low associatio with subsystems S ad S as it was aimed for. Figure 6(d) presets the accuracy of the Xfig recovery process i terms of the Precisio ad Recall metrics. The subsystem S-S4 recovers all the drawig files ad together with S3 recover almost all the editig ad utility files. S is allocated to widowig files ad S recovers file-maipulatio files. The obtaied Precisio ad Recall values idicate the accuracy for the proposed patter matchig techique. Coclusio This paper cotributes to the reverse egieerig research area by providig a iteractive eviromet for architectural recovery, a icremetal graph patter matchig model of the recovery process, ad a prototype toolkit to support the proposed methodology. The proposed eviromet is based o techiques from the areas of data miig, approximate graph matchig, clusterig, ad programmig laguage desig. Refereces [] Rigi, URL = [] Xfig, URL = [3] M. A. Eshera ad K. S. Fu. A similarity measure betwee attributed relatioal graphs for image aalysis. I Seveth Iteratioal Coferece o Patter Recogitio, pages, 84. [4] P. Fiiga, R. Holt, I. Kalas, S. Kerr, K. Kotogiais, et al. The software bookshelf. IBM Systems Joural, 36(4):64 3, November. [] R. Holt, A. Witer, ad A. Schurr. Gxl: Toward a stadard exchage format. I Proceedigs of the WCRE 00, pages 6, 000. [6] R. Kazma ad M. Burth. Assessig architectural complexity. I Proceedigs of the CSMR, pages 04, 8. [] R. Kazma ad S. J. Carriere. Playig detective: Recostructio software architecture from available evidece. Techical Report CMU/SEI--TR-00, Caregie Mello Uiversity,. [8] A. Lakhotia. A uified framework for expressig software subsystem classificatio techiques. Joural of Systems ad Software, 36(3): 3,. [] S. Macoridis, et. al. Usig automatic clusterig to produce high-level system orgaizatios of source code. I Proceedigs of the IWPC, pages 4 3, 8. [0] G. C. Murphy, D. Notki, ad K. Sulliva. Software reflexio model: Bridgig the gap betwee source ad higher-level models. I I proceedigs of the 3rd ACM SIGSOFT SFSE, pages 8 8,. [] K. Sartipi. Alborz: A query-based tool for software architecture recovery. I Proceedigs of the IWPC 0, pages 6, 00. [] K. Sartipi. Software Architecture Recovery based o Patter Matchig. PhD thesis, School of Computer Sciece, Uiversity of Waterloo, Waterloo, ON, Caada, 003. [3] K. Sartipi ad K. Kotogiais. Compoet clusterig based o maximal associatio. I Proceedigs of the IEEE WCRE 0, pages 03 4, 00. [4] K. Sartipi ad K. Kotogiais. A graph patter matchig approach to software architecture recovery. I Proceedigs of the IEEE ICSM 0, pages 408 4, Italy, 00. [] M. Siff ad T. Reps. Idetifyig modules via cocept aalysis. IEEE Trasactios o Software Egieerig, (6):4 68, Nov./Dec.. [6] S. G. Woods, A. Quilici, ad Q. Yag. Costrait-Based Desig recovery for Software Reegieerig: Theory ad Experimets. Kluwer Academic Publishers, 8.