Constant Inapproximability for PPA

Deligkas, Argyrios, Fearnley, John, Hollender, Alexandros and Melissourgos, Themistoklis (2022) Constant Inapproximability for PPA. In: STOC '22: 54th Annual ACM SIGACT Symposium on Theory of Computing.

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Abstract

In the ϵ-Consensus-Halving problem, we are given n probability measures v1, ..., vn on the interval R = [0,1], and the goal is to partition R into two parts R+ and R- using at most n cuts, so that |vi(R+)-vi(R-)| ≤ ϵ for all i. This fundamental fair division problem was the first natural problem shown to be complete for the class PPA, and all subsequent PPA-completeness results for other natural problems have been obtained by reducing from it. We show that ϵ-Consensus-Halving is PPA-complete even when the parameter ϵ is a constant. In fact, we prove that this holds for any constant ϵ < 1/5. As a result, we obtain constant inapproximability results for all known natural PPA-complete problems, including Necklace-Splitting, the Discrete-Ham-Sandwich problem, two variants of the pizza sharing problem, and for finding fair independent sets in cycles and paths.

Item Type:	Conference or Workshop Item (Unspecified)
Uncontrolled Keywords:	TFNP, PPA, fair division, consensus halving, ham sandwich theorem
Divisions:	Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	07 Mar 2022 16:23
Last Modified:	24 Nov 2023 03:00
DOI:	10.1145/3519935.3520079
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3150309