Restricted Max-Min Fair Allocation

04/29/2018

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by   Siu-Wing Cheng, et al.

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The restricted max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. It is NP-hard to approximate the problem to a ratio less than 2. Comparing the current best algorithm for estimating the optimal value with the current best for constructing an allocation, there is quite a gap between the ratios that can be achieved in polynomial time: 4+δ for estimation and 6 + 2√(10) + δ≈ 12.325 + δ for construction, where δ is an arbitrarily small constant greater than 0. We propose an algorithm that constructs an allocation with value within a factor 6 + δ from the optimum for any constant δ > 0. The running time is polynomial in the input size for any constant δ chosen.