Integrality Gap of the Configuration LP for the Restricted Max-Min Fair Allocation
Abstract
The max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. Each player $p$ has a non-negative value $v_{pr}$ on resource $r$. In the restricted case, we have $v_{pr}\in \{v_r, 0\}$. That is, a resource $r$ is worth value $v_r$ for the players who desire it and value 0 for the other players. In this paper, we consider the configuration LP, a linear programming relaxation for the restricted problem. The integrality gap of the configuration LP is at least $2$. Asadpour, Feige, and Saberi proved an upper bound of $4$. We improve the upper bound to $23/6$ using the dual of the configuration LP. Since the configuration LP can be solved to any desired accuracy $\delta$ in polynomial time, our result leads to a polynomial-time algorithm which estimates the optimal value within a factor of $23/6+\delta$.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2018
- DOI:
- 10.48550/arXiv.1807.04152
- arXiv:
- arXiv:1807.04152
- Bibcode:
- 2018arXiv180704152C
- Keywords:
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- Computer Science - Data Structures and Algorithms