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DOI: 10.4230/LIPIcs.ICALP.2019.138
URN: urn:nbn:de:0030-drops-107141
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10714/
Deligkas, Argyrios ; Fearnley, John ; Melissourgos, Themistoklis ; Spirakis, Paul G.
Computing Exact Solutions of Consensus Halving and the Borsuk-Ulam Theorem
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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 [Filos-Ratsikas and Goldberg, 2018; Filos-Ratsikas and Goldberg, 2018], 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. 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.
BibTeX - Entry
@InProceedings{deligkas_et_al:LIPIcs:2019:10714,
author = {Argyrios Deligkas and John Fearnley and Themistoklis Melissourgos and Paul G. Spirakis},
title = {{Computing Exact Solutions of Consensus Halving and the Borsuk-Ulam Theorem}},
booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
pages = {138:1--138:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-109-2},
ISSN = {1868-8969},
year = {2019},
volume = {132},
editor = {Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10714},
URN = {urn:nbn:de:0030-drops-107141},
doi = {10.4230/LIPIcs.ICALP.2019.138},
annote = {Keywords: PPA, FIXP, ETR, consensus halving, circuit, reduction, complexity class}
}
| Keywords: | PPA, FIXP, ETR, consensus halving, circuit, reduction, complexity class | |
| Seminar: | 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 04.07.2019 |
