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arXiv · 1609.05136

Hardness Results for Consensus-Halving

Aris Filos-Ratsikas·Soren Kristoffer Stiil Frederiksen·Paul W. Goldberg·Jie Zhang
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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 $\epsilon$-approximate consensus-halving problem allows each agent to have an $\epsilon$ discrepancy on the values of the portions. We prove that computing $\epsilon$-approximate consensus-halving solution using $n$ cuts is in PPA, and is PPAD-hard, where $\epsilon$ 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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Aris Filos-Ratsikas, Soren Kristoffer Stiil Frederiksen, Paul W. Goldberg, Jie Zhang. 2016-09-16. Hardness Results for Consensus-Halving. https://arxiv.org/abs/1609.05136

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