Minimum non-submodular cover problem with applications '

Minimum Submodular Cover problem often occurs naturally in the context of combinatorial optimization. It is well-known that the greedy algorithm achieves an H(delta)- approximation guarantee for an integer-valued polymatroid potential function f, where delta is the maximum value of f over all singletons and H(delta) is the delta-th harmonic number. In this paper, we extend the setting into the non-submodular potential functions and investigate Minimum Non-submodular Cover problem with integer-valued and fraction valued potential functions respectively, yielding similar performance results. In addition, we address several real-world applications which can be formulated as Minimum Nonsubmodular Cover problem. (C) 2021 Elsevier Inc. All rights reserved.