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arXiv · 1905.06084

Restricted Max-Min Allocation: Approximation and Integrality Gap

Siu-Wing Cheng·Yuchen Mao
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Abstract

Asadpour, Feige, and Saberi proved that the integrality gap of the configuration LP for the restricted max-min allocation problem is at most $4$. However, their proof does not give a polynomial-time approximation algorithm. A lot of efforts have been devoted to designing an efficient algorithm whose approximation ratio can match this upper bound for the integrality gap. In ICALP 2018, we present a $(6 + δ)$-approximation algorithm where $δ$ can be any positive constant, and there is still a gap of roughly $2$. In this paper, we narrow the gap significantly by proposing a $(4+δ)$-approximation algorithm where $δ$ can be any positive constant. The approximation ratio is with respect to the optimal value of the configuration LP, and the running time is $\mathit{poly}(m,n)\cdot n^{\mathit{poly}(\frac{1}δ)}$ where $n$ is the number of players and $m$ is the number of resources. We also improve the upper bound for the integrality gap of the configuration LP to $3 + \frac{21}{26} \approx 3.808$.

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Siu-Wing Cheng, Yuchen Mao. 2019-05-15. Restricted Max-Min Allocation: Approximation and Integrality Gap. https://arxiv.org/abs/1905.06084

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