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Hardness results for consensus-halving

Hardness results for consensus-halving
Hardness results for consensus-halving
We study the consensus-halving problem of dividing an object into two portions, such that each of n agents has equal valuation for the two portions. The ϵ-approximate consensus-halving problem allows each agent to have an ϵ discrepancy on the values of the portions. We prove that computing ϵ-approximate consensus-halving solution using n cuts is in PPA, and is PPAD-hard, where ϵ is some positive constant; the problem remains PPAD-hard when we allow a constant number of additional cuts. It is NP-hard to decide whether a solution with n−1 cuts exists for the problem. As a corollary of our results, we obtain that the approximate computational version of the Continuous Necklace Splitting Problem is PPAD-hard when the number of portions t is two.
Leibniz International Proceedings in Informatics (LIPIcs)
Filos-Ratsikas, Aris
14e554b2-bc6b-4b2c-a84d-8650ad4bed14
Søren Kristoffer, Stiil Frederiksen
48ffcf47-134e-44ce-a968-bf3bc0247cc8
Goldberg, Paul W.
46b110bb-a7df-406d-babc-291a17fff863
Zhang, Jie
6bad4e75-40e0-4ea3-866d-58c8018b225a
Filos-Ratsikas, Aris
14e554b2-bc6b-4b2c-a84d-8650ad4bed14
Søren Kristoffer, Stiil Frederiksen
48ffcf47-134e-44ce-a968-bf3bc0247cc8
Goldberg, Paul W.
46b110bb-a7df-406d-babc-291a17fff863
Zhang, Jie
6bad4e75-40e0-4ea3-866d-58c8018b225a

Filos-Ratsikas, Aris, Søren Kristoffer, Stiil Frederiksen, Goldberg, Paul W. and Zhang, Jie (2018) Hardness results for consensus-halving. In 43rd International Symposium on Mathematical Foundations of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs).. (In Press)

Record type: Conference or Workshop Item (Paper)

Abstract

We study the consensus-halving problem of dividing an object into two portions, such that each of n agents has equal valuation for the two portions. The ϵ-approximate consensus-halving problem allows each agent to have an ϵ discrepancy on the values of the portions. We prove that computing ϵ-approximate consensus-halving solution using n cuts is in PPA, and is PPAD-hard, where ϵ is some positive constant; the problem remains PPAD-hard when we allow a constant number of additional cuts. It is NP-hard to decide whether a solution with n−1 cuts exists for the problem. As a corollary of our results, we obtain that the approximate computational version of the Continuous Necklace Splitting Problem is PPAD-hard when the number of portions t is two.

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Accepted/In Press date: 15 June 2018

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Local EPrints ID: 422938
URI: http://eprints.soton.ac.uk/id/eprint/422938
PURE UUID: 430c88ef-6448-4c19-a1e6-d58d4f857962

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Date deposited: 08 Aug 2018 16:30
Last modified: 11 Mar 2022 02:53

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Contributors

Author: Aris Filos-Ratsikas
Author: Stiil Frederiksen Søren Kristoffer
Author: Paul W. Goldberg
Author: Jie Zhang

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