Approximate Graph Matching in Software Engineering

Abstract

Graph representations are among the most common and effective ways to model all kinds of natural or human-made objects. Once two objects or problems have been represented as graphs (i.e. as collections of objects possibly connected by pairwise relations), their comparison is a fundamental question in many different applications and is often addressed using graph matching. The work presented in this document investigates approximate graph matching techniques and their application in software engineering, notably as efficient ways to retrieve the evolution through time of software artifacts. The research work we carried involves three distinct but related aspects. First, we consider approximate graph matching problems within the Error-Tolerant Graph Matching framework, and propose a tabu search technique initialized with local structural similarity measures. Second, we address the matching of software artifacts, such as class diagrams, and propose new concepts able to integrate efficiently the lexical information, found in typical diagrams, to our tabu search. Third, based on matchings obtained from the application of our approach to subsequent class diagrams, we proposed new design evolution metrics and assessed their usefulness in defect prediction models. The following paragraphs detail each of those three aspects.Approximate Graph Matching Many practical problems can be modeled as approximate graph matching (AGM) problems in which the goal is to find a "good" matching between two objects represented as graphs. Unfortunately, existing literature on AGM does not propose generic techniques readily usable in research areas other than image processing and biochemistry. To address this situation, we tackled in a generic way, the AGM problems. For this purpose, we first select, out of the possible formulations, the Error Tolerant Graph Matching (ETGM) framework, which is able to model most AGM formulations. Given that AGM problems are generally NP-hard, we based our resolution approach on meta-heuristics, given the demonstrated efficiency of this family of techniques on (NP-)hard problems. Our approach avoids as much as possible assumptions about graphs to be matched and tries to make the best out of basic graph features such as node connectivity and edge types. Consequently, the proposal is a local search technique using new node similarity measures derived from simple structural information. The proposed technique was devised as follows. First, we observed and empirically validated that initializing a local search with a very small subset of "correct" node matches is enough to get excellent results. Thus, instead of directly trying to correctly match all nodes and edges from two graphs, one could focus on correctly matching a few nodes. Second, in order to retrieve such node matches, we resorted to the concept of local node similarity which consists in analyzing viii nodes' neighborhoods to assess for each possible node match the likelihood of its inclusion in a good matching. We investigated many ways of c...

MADMatch: Many-to-Many Approximate Diagram Matching for Design Comparison

“…The best configuration is chosen, while avoiding returning 3. Details are provided in [16] toward solutions recently visited by using a shortterm tabu list. When, after a certain number of iterations, there is no longer improvement with respect to the best solution found so far, the search is stopped and the solution with the minimal cost is returned.…”

“…We first report the settings of MADMatch and our procedure for compared evaluations, then present the different case studies. Note that, out of space considerations, we only reported key results and we refer the reader to [16] for more details.…”

“…To ease this task, MADMatch produces detailed csv files informing about a considered match (see [16] for more details). Still, in many cases, it remains difficult to decide if a match is right and we had to resort to a more time-consuming option: the exploration of the source code.…”

“…Most of the correct node matches brought by matches exclusive to one algorithm come from the sets of MADMatch with medians of 100%, 82%, and 74% respectively for DNSJava, JFreeChart, and ArgoUML. Detailed results obtained on each program are available in [16].…”

“…We selected versions 1.2 and 2.0 (the first two versions for which we have modeling data) of EasyCoin and three sequence diagrams out of those versions: InserireEnteEmettitore and ModificareEnteEmettitore (from version 1.2) and InserireEnteEmettitore (from version 2.0) 16 Figure 8 presents the matching of the two subsequent versions of InserireEnteEmettitore. Except for a merge, all objects are perfectly matched.…”