On the variable ordering in subgraph isomorphism algorithms

Graphs are mathematical structures to model several biological data. Applications to analyze them require to apply solutions for the subgraph isomorphism problem, which is NP-complete. Here, we investigate the existing strategies to reduce the subgraph isomorphism algorithm running time with emphasis on the importance of the order with which the graph vertices are taken into account during the search, called variable ordering, and its incidence on the total running time of the algorithms. We focus on two recent solutions, which are based on an effective variable ordering strategy. We discuss their comparison both with the variable ordering strategies reviewed in the paper and the other algorithms present in the ICPR2014 contest on graph matching algorithms for pattern search in biological databases.