Partitioning Biological Networks into Highly Connected Clusters with Maximum Edge Coverage
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.
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