Efficient $\Theta$-Subsumption Based on Graph Algorithms

The $\theta$-subsumption problem is crucial to the efficiency of ILP learning systems. We discuss two $\theta$-subsumption algorithms based on strategies for preselecting suitable matching literals. The class of clauses, for which subsumption becomes polynomial, is a superset of the deterministic clauses. We further map the general problem of $\theta$-subsumption to a certain problem of finding a clique of fixed size in a graph, and in return show that a specialization of the pruning strategy of the Carraghan and Pardalos clique algorithm provides a dramatic reduction of the subsumption search space. We also present empirical results for the mesh design data set.