Partitioning biological networks into highly connected clusters with maximum edge coverage

Abstract

We introduce the combinatorial optimization problem Highly Connected Deletion, which asks for removing as few edges as possible from a graph such that the resulting graph consists of highly connected components. We show that Highly Connected Deletion is NP-hard and provide a fixed-parameter algorithm and a kernelization. We propose exact and heuristic solution strategies, based on polynomial-time data reduction rules and integer linear programming with column generation. The data reduction typically identifies 85 % of the edges that need to be deleted for an optimal solution; the column generation method can then optimally solve protein interaction networks with up to 5 000 vertices and 12 000 edges. © 2013 Springer-Verlag.