文章基本信息

标题：Hardness Results for Consensus-Halving
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作者：Aris Filos-Ratsikas ; S\oren Kristoffer Stiil Frederiksen ; Paul W. Goldberg 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2018
卷号：117
页码：1-16
DOI：10.4230/LIPIcs.MFCS.2018.24
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：The Consensus-halving problem is the problem of dividing an object into two portions, such that each of n agents has equal valuation for the two portions. We study the epsilon-approximate version, which allows each agent to have an epsilon discrepancy on the values of the portions. It was recently proven in [Filos-Ratsikas and Goldberg, 2018] that the problem of computing an epsilon-approximate Consensus-halving solution (for n agents and n cuts) is PPA-complete when epsilon is inverse-exponential. In this paper, we prove that when epsilon is constant, the problem is PPAD-hard and the problem remains PPAD-hard when we allow a constant number of additional cuts. Additionally, we prove that deciding whether a solution with n-1 cuts exists for the problem is NP-hard.
关键词：PPAD; PPA; consensus halving; generalized-circuit; reduction