Experimental Evaluation of Subgraph Isomorphism Solvers

International audienceSubgraph Isomorphism (SI) is an NP-complete problem which is at the heart of many structural pattern recognition tasks as it involves finding a copy of a pattern graph into a target graph. In the pattern recognition community, the most well-known SI solvers are VF2, VF3, and RI. SI is also widely studied in the constraint programming community, and many constraint-based SI solvers have been proposed since Ullman, such as LAD and Glasgow, for example. All these SI solvers can solve very quickly some large SI instances, that involve graphs with thousands of nodes. However, McCreesh et al. have recently shown how to randomly generate SI instances the hardness of which can be controlled and predicted, and they have built small instances which are computationally challenging for all solvers. They have also shown that some small instances, which are predicted to be easy and are easily solved by constraint-based solvers, appear to be challenging for VF2 and VF3. In this paper, we widen this study by considering a large test suite coming from eight benchmarks. We show that, as expected for an NP-complete problem, the solving time of an instance does not depend on its size, and that some small instances coming from real applications are not solved by any of the considered solvers. We also show that, if RI and VF3 can solve very quickly a large number of easy instances, for which Glasgow or LAD need more time, they fail at solving some other instances that are quickly solved by Glasgow or LAD, and they are clearly outperformed by Glasgow on hard instances. Finally, we show that we can easily combine solvers to take benefit of their complementarity

Parallel Searching on Biological Networks

Software applications for biological networks analysis rely on graphs to model the structure interactions. A great part of them requires searching for subgraphs in a target graph or in collections of graphs. Even though very efficient algorithms have been defined to solve such a subgraph isomorphisms problem, the complexity of current real biological networks make their sequential execution time prohibitive. On the other hand, parallel architectures, from multi-core to many-core, have become pervasive to deal with the problem of the data size. Nevertheless, the sequential nature of the graph searching algorithms makes their implementation for parallel architectures very challenging. This paper presents three different parallel solutions for the graph searching problem. The first two target the exact search for multi-core CPUs and many-core GPUs, respectively. The third one targets the approximate search for GPUs, which handles node, edge, and node label mismatches. The paper shows how different techniques have been developed in all the solutions to reduce the search space complexity. The paper shows the performance of the proposed solutions on representative biological networks containing antiviral chemical compounds and protein interactions networks