Abstract
Minimum Submodular Cover problem often occurs naturally in the context of combinatorial optimization. It is well-known that the greedy algorithm achieves an H(δ)-approximation guarantee for an integer-valued polymatroid potential function f, where δ is the maximum value of f over all singletons and H(δ) is the δ-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 Non-submodular Cover problem.
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