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
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
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
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
The Complexity of Perfect Matching Problems on Dense Hypergraphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On linear and semidefinite programming relaxations for hypergraph matching
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
An Approximation Algorithm for Max-Min Fair Allocation of Indivisible Goods
SIAM Journal on Computing
Santa Claus schedules jobs on unrelated machines
Proceedings of the forty-third annual ACM symposium on Theory of computing
On the configuration-LP for scheduling on unrelated machines
ESA'11 Proceedings of the 19th European conference on Algorithms
New Constructive Aspects of the Lovász Local Lemma
Journal of the ACM (JACM)
Santa claus meets hypergraph matchings
ACM Transactions on Algorithms (TALG)
Quasi-polynomial local search for restricted max-min fair allocation
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
European Journal of Combinatorics
Polynomial-time perfect matchings in dense hypergraphs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We consider the problem of max-min fair allocation of indivisible goods. Our focus will be on the restricted version of the problem in which there are mitems, each of which associated with a non-negative value. There are also nplayers and each player is only interested in some of the items. The goal is to distribute the items between the players such that the least happy person is as happy as possible, i.e. one wants to maximize the minimum of the sum of the values of the items given to any player. This problem is also known as the Santa Claus problem[3]. Feige [9] proves that the integrality gap of a certain configuration LP, described by Bansal and Sviridenko [3], is bounded from below by some (unspecified) constant. This gives an efficient way to estimate the optimum value of the problem within a constant factor. However, the proof in [9] is nonconstructive: it uses the Lovasz local lemma and does not provide a polynomial time algorithm for finding an allocation. In this paper, we take a different approach to this problem, 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 bounded by $\frac{1}{5}$. Our proof is nonconstructive in the following sense: it does provide a local search algorithm which finds the corresponding allocation, but this algorithm is not known to converge to a local optimum in a polynomial number of steps.