A parameterized algorithm for packing overlapping subgraphs

Abstract

Finding subgraphs with arbitrary overlap was introduced as the k-H-Packing with t-Overlap problem in [10]. Specifically, does a given graph G have at least k induced subgraphs each isomorphic to a graph H such that any pair of subgraphs share at most t vertices? This problem has applications in the discovering of overlapping communities in real networks. In this work, we introduce the first parameterized algorithm for the k-H-Packing with t-Overlap problem when H is an arbitrary graph of size r. Our algorithm combines a bounded search tree with a greedy localization technique and runs in time O(r rk k (r∈-∈t∈-∈1)k∈+∈2 n r ), where n∈=∈|V(G)|, r∈=∈|V(H)|, and t∈