Heuristics and Really Hard Instances for Subgraph Isomorphism Problems

We show how to generate “really hard” random instances for subgraph isomorphism problems. For the non-induced variant, we predict and observe a phase transition between satisfiable and unsatis- fiable instances, with a corresponding complexity peak seen in three different solvers. For the induced variant, much richer behaviour is observed, and constrainedness gives a better measure of difficulty than does proximity to a phase transition. We also discuss variable and value ordering heuristics, and their relationship to the expected number of solutions