Approximation algorithms for connected maximum coverage problem for the discovery of mutated driver pathways in cancer

Abstract This paper addresses the connected maximum coverage problem, motivated by the detection of mutated driver pathways in cancer. The connected maximum coverage problem is NP-hard and therefore approximation algorithms are of interest. We provide here an approximation algorithm for the problem with an approximation bound that strictly improves on previous results. A second approximation algorithm with faster run time, though worse approximation factor, is presented as well. The two algorithms are then applied to submodular maximization over a connected subgraph, with a monotone submodular set function, delivering the same approximation bounds as for the coverage maximization case.