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 < r. Applying similar ideas we also obtain an algorithm for packing sets with possible overlap which is a version of the k-Set Packing problem.
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