Estudo experimental da aplicação do algoritmo IVL na etapa de detecção de isomorfismos do GROOVE

Abstract

The graph isomorphism is a classical problem in Graph Theory, which consists of determining if, given two graphs, it is possible to define a mapping between their vertexes in a way so that the connection defined by their edges are respected. An algorithm proposed recently to solve this problem is the IVL (Iterated Vertex Labelling) [Baroni (2012)]. GROOVE (GRaph-based Object-Oriented VErification) is a graph-based model checking tool which makes use of isomorphism algorithms. In GROOVE’s context, the graph isomorphism problem is set differently from the classical problem: they are not interested on determining if two graphs are isomorphic, instead, they want to determine if, given a graph, it is isomorphic to one of the elements of a graph set. In this work, it’s proposed the IVL adaptation to GROOVE and computational experiments in order to test if this new adapted algorithm brings performance gains to the tool. It can be concluded from the results that IVL has a similar performance compared to the current implementation in GROOVE. Beyond those results, it was investigated in a similar framework the use of non-isomorphism filters, intending to determine the non-isomorphism between two graphs in a low computational cost. The test results point out that this is a promising approach, being able to detect non-isomorphisms with almost 100% efficiency, with a much lower running time when compared to current GROOVE algorithm when executed in this framework.