eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-08-27
24:1
24:16
10.4230/LIPIcs.MFCS.2018.24
article
Hardness Results for Consensus-Halving
Filos-Ratsikas, Aris
1
Frederiksen, Søren Kristoffer Stiil
2
Goldberg, Paul W.
3
Zhang, Jie
4
École Polytechnique Fédérale de Lausanne, Switzerland
Aarhus University, Denmark
University of Oxford, United Kingdom
University of Southampton, United Kingdom
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol117-mfcs2018/LIPIcs.MFCS.2018.24/LIPIcs.MFCS.2018.24.pdf
PPAD
PPA
consensus halving
generalized-circuit
reduction