Deligkas, Argyrios, Fearnley, John, Melissourgos, Themistoklis ORCID: 0000-0002-9867-6257 and Spirakis, Paul G ORCID: 0000-0001-5396-3749
(2019)
Computing Exact Solutions of Consensus Halving and the Borsuk-Ulam
Theorem.
Leibniz International Proceedings in Informatics, LIPIcs, 132.
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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, 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.
Item Type: | Article |
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Uncontrolled Keywords: | cs.CC, cs.CC, math.AT |
Depositing User: | Symplectic Admin |
Date Deposited: | 30 Jan 2020 14:08 |
Last Modified: | 19 Jan 2023 00:05 |
DOI: | 10.4230/LIPIcs.ICALP.2019.138 |
Open Access URL: | https://arxiv.org/abs/1903.03101 |
Related URLs: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3072700 |
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Computing Exact Solutions of Consensus Halving and the Borsuk-Ulam Theorem. (deposited 11 Mar 2019 08:38)
- Computing Exact Solutions of Consensus Halving and the Borsuk-Ulam Theorem. (deposited 30 Jan 2020 14:08) [Currently Displayed]