Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 410, Issue -, Pages -Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2021.126442
Keywords
Greedy algorithm; Submodular function; Submodular cover; Approximation ratio
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The extension of Minimum Submodular Cover problem to non-submodular potential functions, along with the investigation of Minimum Non-submodular Cover problem with integer-valued and fraction valued potential functions, yield similar performance results. The paper also addresses several real-world applications that can be formulated as Minimum Nonsubmodular Cover problem.
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.
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