Making an arbitrary filled graph minimal by removing fill edges

Abstract

We consider the problem of removing fill edges from a filled graph G′ to get a minimal chordal supergraph M of the original graph G; thus G ⊆ M ⊆ G′. We show that a greedy strategy can be applied if fill edges are processed for removal in the reverse order of their introduction. For a filled graph with f fill edges and e original edges, we give a simple O(f(e + f)) algorithm which solves the problem and computes a corresponding minimal elimination ordering. We believe that in practice the runtime of our algorithm is usually better than the worst-case bound of O(f(e + f).