When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2018.24
URN: urn:nbn:de:0030-drops-96069
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9606/
 Go to the corresponding LIPIcs Volume Portal

### Hardness Results for Consensus-Halving

 pdf-format:

### Abstract

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.

### BibTeX - Entry

```@InProceedings{filosratsikas_et_al:LIPIcs:2018:9606,
author =	{Aris Filos-Ratsikas and S\oren Kristoffer Stiil Frederiksen and Paul W. Goldberg and Jie Zhang},
title =	{{Hardness Results for Consensus-Halving}},
booktitle =	{43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)},
pages =	{24:1--24:16},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-086-6},
ISSN =	{1868-8969},
year =	{2018},
volume =	{117},
editor =	{Igor Potapov and Paul Spirakis and James Worrell},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},