Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
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
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
On allocations that maximize fairness
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Graph balancing: a special case of scheduling unrelated parallel machines
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
Hall's theorem for hypergraphs
Journal of Graph Theory
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
On Maximizing Welfare When Utility Functions Are Subadditive
SIAM Journal on Computing
An Approximation Algorithm for Max-Min Fair Allocation of Indivisible Goods
SIAM Journal on Computing
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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We consider the restricted assignment version of the problem of max-min fair allocation of indivisible goods, also known as the Santa Claus problem. There are m items and n players. Every item has some nonnegative value, and every player is interested in only some of the items. The goal is to distribute the items to the players in a way that maximizes the minimum of the sum of the values of the items given to any player. It was previously shown via a nonconstructive proof that uses the Lovász local lemma that the integrality gap of a certain configuration LP for the problem is no worse than some (unspecified) constant. This gives a polynomial-time algorithm to estimate the optimum value of the problem within a constant factor, but does not provide a polynomial-time algorithm for finding a corresponding allocation. We use a different approach to analyze the integrality gap. Our approach is based upon local search techniques for finding perfect matchings in certain classes of hypergraphs. As a result, we prove that the integrality gap of the configuration LP is no worse than 1/4. Our proof provides a local search algorithm which finds the corresponding allocation, but is nonconstructive in the sense that this algorithm is not known to converge to a local optimum in a polynomial number of steps.