On allocations that maximize fairness

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On allocations that maximize fairness
We consider a problem known as the restricted assignment version of the max-min allocation problem with indivisible goods. There are n items of various nonnegative values and m players. Every player is interested only in some of the items and has zero value for the other items. One has to distribute the items among the players in a way that maximizes a certain notion of fairness, namely, maximizes the minimum of the sum of values of items given to any player. Bansal and Sviridenko [STOC 2006] describe a linear programming relaxation for this problem, and present a rounding technique that recovers an allocation of value at least (log log log m/ log log m) of the optimum. We show that the value of this LP relaxation in fact approximates the optimum value to within a constant factor. Our proof is not constructive and does not by itself provide an efficient algorithm for finding an allocation that is within constant factors of optimal.
Uriel Feige
Added 30 Oct 2010
Updated 30 Oct 2010
Type Conference
Year 2008
Where SODA
Authors Uriel Feige
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