Abstract
Edge cover games are cooperative cost games arising from edge cover problems, where each player controls a vertex and the cost of a coalition is the minimum weight of edge covers in the subgraph induced by the coalition. In this paper, we study the approximate core for edge cover games. We show that the ratio of approximate core depends on the shortest odd cycle of underlying graphs and the \(\frac{3}{4}\)-core is always non-empty. We also show that the approximate ratio \(\frac{3}{4}\) is tight, since it coincides with the integrality gap of the natural LP for edge cover problems.
This work is supported in part by the National Natural Science Foundation of China (Nos. 12001507, 11871442, 11971447 and 12171444) and Natural Science Foundation of Shandong (No. ZR2020QA024).
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We would like to extend our sincere thanks to the anonymous reviewers for their thorough and constructive feedback, which helped us significantly improve the quality of this manuscript.
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Lu, T., Xiao, H., Fang, Q. (2023). Approximate Core Allocations for Edge Cover Games. In: Li, M., Sun, X., Wu, X. (eds) Frontiers of Algorithmics. IJTCS-FAW 2023. Lecture Notes in Computer Science, vol 13933. Springer, Cham. https://doi.org/10.1007/978-3-031-39344-0_8
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