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New Algorithmic Aspects of the Local Lemma with Applications to Routing and Partitioning
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On approximately fair allocations of indivisible goods
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
Optimal on-line algorithms for the uniform machine scheduling problem with ordinal data
Information and Computation
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ADT '09 Proceedings of the 1st International Conference on Algorithmic Decision Theory
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The Efficiency of Fair Division
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Min sum edge coloring in multigraphs via configuration LP
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Maximizing the minimum load for selfish agents
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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ACM Transactions on Algorithms (TALG)
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SocInfo'10 Proceedings of the Second international conference on Social informatics
An Approximation Algorithm for Max-Min Fair Allocation of Indivisible Goods
SIAM Journal on Computing
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Journal of Combinatorial Optimization
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We consider the following problem: The Santa Claus has n presents that he wants to distribute among m kids. Each kid has an arbitrary value for each present. Let pij be the value that kid i has for present j. The Santa's goal is to distribute presents in such a way that the least lucky kid is as happy as possible, i.e he tries to maximize mini=1,...,m sumj ∈ Si pij where Si is a set of presents received by the i-th kid.Our main result is an O(log log m/log log log m) approximation algorithm for the restricted assignment case of the problem when pij ∈ pj,0 (i.e. when present j has either value pj or 0 for each kid). Our algorithm is based on rounding a certain natural exponentially large linear programming relaxation usually referred to as the configuration LP. We also show that the configuration LP has an integrality gap of Ω(m1/2) in the general case, when pij can be arbitrary.