Approximate Cores of Submodular Cost Set Cover Games

Qingqin Nong, Jingyu Yao, Xin Qin, Suning Gong () and Qizhi Fang
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Qingqin Nong: Ocean University of China
Jingyu Yao: Ocean University of China
Xin Qin: Ocean University of China
Suning Gong: Qingdao University
Qizhi Fang: Ocean University of China

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 3, No 13, 15 pages

Abstract: Abstract This paper considers approximate cores of submodular cost set cover games. A submodular cost set cover game involves a finite set of players, an index set, and a submodular function defined on the index set. Each element in the index set corresponds to a subset of the player set and the union of all these subsets equals the entire player set. Given a subset of players, call a subset of the index set a cover of it if the union of the corresponding sets contains all the players in the subset. For any subset of players, its cost is the minimum submodular function value over all possible set covers of the subset. In this paper, we study the non-emptiness property of the approximate cores of submodular cost set cover games from the perspective of the integrality gap of the mathematical program for submodular cost set cover optimization problems.

Keywords: Submodular; Set cover; Game; Approximate core; Integrality gap; 91A12; 90C27; 68W25 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02806-1

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