On the Complexity of Chore Division

Alireza Farhadi; MohammadTaghi Hajiaghayi

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arXiv · 1710.00271

On the Complexity of Chore Division

Alireza Farhadi·MohammadTaghi Hajiaghayi

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Abstract

We study the proportional chore division problem where a protocol wants to divide an undesirable object, called chore, among $n$ different players. The goal is to find an allocation such that the cost of the chore assigned to each player be at most $1/n$ of the total cost. This problem is the dual variant of the cake cutting problem in which we want to allocate a desirable object. Edmonds and Pruhs showed that any protocol for the proportional cake cutting must use at least $\Omega(n \log n)$ queries in the worst case, however, finding a lower bound for the proportional chore division remained an interesting open problem. We show that chore division and cake cutting problems are closely related to each other and provide an $\Omega(n \log n)$ lower bound for chore division.

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BibTeX RIS

Alireza Farhadi, MohammadTaghi Hajiaghayi. 2017-09-30. On the Complexity of Chore Division. https://arxiv.org/abs/1710.00271

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