Efficient theta-subsumption based on graph algorithms

The θ-subsumption problem is crucial to the efficiency of ILP learning systems. We discuss two θ-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 θ-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.