Computing exact solutions of consensus halving and the Borsuk-Ulam theorem

Deligkas, Argyrios, Fearnley, John, Melissourgos, Themistoklis ORCID: 0000-0002-9867-6257 and Spirakis, Paul G ORCID: 0000-0001-5396-3749 (2021) Computing exact solutions of consensus halving and the Borsuk-Ulam theorem. In: ICALP 2019.

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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 [29,30], we show that the exact version is much harder. Specifically, finding a solution with n agents and n cuts is FIXP -hard, and deciding whether there exists a solution with fewer than n cuts is ETR -complete. Along the way, we define a new complexity class, called BU, which captures all problems that can be reduced to solving an instance of the Borsuk-Ulam problem exactly. We show that FIXP⊆BU⊆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.

Item Type:	Conference or Workshop Item (Unspecified)
Uncontrolled Keywords:	PPA, FIXP, ETR, Consensus halving, Circuit, Reduction, Complexity class
Depositing User:	Symplectic Admin
Date Deposited:	29 Apr 2019 07:59
Last Modified:	19 Jan 2023 00:53
DOI:	10.1016/j.jcss.2020.10.006
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3038523