QuasiPolynomial Local Search for Restricted MaxMin Fair Allocation
Abstract
The restricted maxmin 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. proved that a certain configuration LP can be used to estimate the optimal value within a factor ${1}/{(4+\epsilon)}$, for any $\epsilon>0$, 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 quasipolynomial approximation algorithm with the mentioned performance guarantee. More specifically, we modify the local search of Asadpour et al. and provide a novel analysis that lets us significantly improve the bound on its running time: from $2^{O(n)}$ to $n^{O(\log n)}$. Our techniques also have the interesting property that although we use the rather complex configuration LP in the analysis, we never actually solve it and therefore the resulting algorithm is purely combinatorial.
 Publication:

arXiv eprints
 Pub Date:
 May 2012
 arXiv:
 arXiv:1205.1373
 Bibcode:
 2012arXiv1205.1373P
 Keywords:

 Computer Science  Data Structures and Algorithms;
 68Q25
 EPrint:
 14 pages, 1 figure