Quasi-Polynomial Local Search for Restricted Max-Min Fair Allocation

The restricted max-min fair allocation problem (also known as the restricted Santa Claus problem) is one of few problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, Asadpour et al. [1] proved that a certain configuration LP can be used to estimate the optimal value within a factor 1/(4 + ), for any > 0, but at the same time it is not known how to efficiently find a solution with a comparable performance guarantee. A natural question that arises from their work is if the difference between these guarantees is inherent or because of a lack of suitable techniques. We address this problem by giving a quasi-polynomial approximation algorithm with the mentioned performance guarantee. More specifically, we modify the local search of [1] and provide a novel analysis that lets us significantly improve the bound on its running time: from 2O(n) to nO(log n) . Our techniques also have the interesting property that although ...

• Type: Journal
• Year: 2016
• Where: TALG
• Authors: Lukás Polácek, Ola Svensson
• Keywords: TALG 2016