Restricted Max-Min Fair Allocation

TL;DR

This paper introduces a polynomial-time algorithm that constructs resource allocations within a factor of approximately 6 of the optimal for the restricted max-min fair allocation problem, improving practical approximation bounds.

Contribution

It presents a new algorithm achieving a near-constant approximation ratio for constructing allocations in the restricted max-min fair allocation problem.

Findings

The algorithm guarantees an allocation within a factor of 6 + δ of the optimum.

It operates in polynomial time for any fixed δ > 0.

It narrows the gap between estimation and construction approximation ratios.

Abstract

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: roughly 4 for estimation and roughly $6 + 2\sqrt{10}$ for construction. We propose an algorithm that constructs an allocation with value within a factor of $6 + \delta$ from the optimum for any constant $\delta > 0$. The running time is polynomial in the input size for any constant $\delta$ chosen.