Approximation Algorithms for the Max-Min Allocation Problem

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 − 1)-approximation algorithm for Max-Min when there are k people with subadditive utility functions. We also give a k/α-approximation algorithm (for α ≤ k/2) if the utility functions are additive and the utility of an item for a person is restricted to 0, 1 or U for some U > 1. The running time of this algorithm depends exponentially on the parameter α. Both the algorithms are combinatorial, simple and easy to analyze.