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• W2921543503 abstract "We study the problem of finding an exact solution to the consensus halving problem. While recent work has shown that the approximate version of this problem is PPA-complete, we show that the exact version is much harder. Specifically, finding a solution with $n$ cuts is FIXP-hard, and deciding whether there exists a solution with fewer than $n$ cuts is ETR-complete. We also give a QPTAS for the case where each agent's valuation is a polynomial. Along the way, we define a new complexity class BU, which captures all problems that can be reduced to solving an instance of the Borsuk-Ulam problem exactly. We show that FIXP $subseteq$ BU $subseteq$ TFETR and that LinearBU $=$ PPA, where LinearBU is the subclass of BU in which the Borsuk-Ulam instance is specified by a linear arithmetic circuit." @default.
• W2921543503 created "2019-03-22" @default.
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• W2921543503 date "2019-03-07" @default.
• W2921543503 modified "2023-09-27" @default.
• W2921543503 title "Computing Exact Solutions of Consensus Halving and the Borsuk-Ulam Theorem" @default.
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