Approximation Algorithms for the Max-Min Allocation Problem

Authors:
Subhash Khot;Ashok Kumar Ponnuswami
Affiliations:
College of Computing, Georgia Institute of Technology, Atlanta GA 30309, USA;College of Computing, Georgia Institute of Technology, Atlanta GA 30309, USA
Venue:
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Year:
2007

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Abstract

The Max-Min allocation problem is to distribute indivisible goods to people so as to maximize the minimum utility of the people. We show a (2k茂戮驴 1)-approximation algorithm for Max-Min when there are kpeople with subadditive utility functions. We also give a k/茂戮驴-approximation algorithm (for 茂戮驴≤ k/2) if the utility functions are additive and the utility of an item for a person is restricted to 0, 1 or Ufor some U 1. The running time of this algorithm depends exponentially on the parameter 茂戮驴. Both the algorithms are combinatorial, simple and easy to analyze.