Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
An improved approximation algorithm for combinatorial auctions with submodular bidders
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
ACM SIGecom Exchanges
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On maximizing welfare when utility functions are subadditive
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Approximation algorithms for allocation problems: Improving the factor of 1 - 1/e
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
An approximation algorithm for max-min fair allocation of indivisible goods
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On allocations that maximize fairness
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal approximation for the submodular welfare problem in the value oracle model
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Santa Claus Meets Hypergraph Matchings
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
MaxMin allocation via degree lower-bounded arborescences
Proceedings of the forty-first annual ACM symposium on Theory of computing
On Allocating Goods to Maximize Fairness
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
New Constructive Aspects of the Lovasz Local Lemma
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Santa Claus schedules jobs on unrelated machines
Proceedings of the forty-third annual ACM symposium on Theory of computing
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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+ε), for any ε0, 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(logn). 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.