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Approximation algorithms for allocation problems: Improving the factor of 1 - 1/e

10 years 5 months ago
Approximation algorithms for allocation problems: Improving the factor of 1 - 1/e
Combinatorial allocation problems require allocating items to players in a way that maximizes the total utility. Two such problems received attention recently, and were addressed using the same linear programming (LP) relaxation. In the Maximum Submodular Welfare (SMW) problem, utility functions of players are submodular, and for this case Dobzinski and Schapira [SODA 2006] showed an approximation ratio of 1 − 1/e. In the Generalized Assignment Problem (GAP) utility functions are linear but players also have capacity constraints. GAP admits a (1 − 1/e)approximation as well, as shown by Fleischer, Goemans, Mirrokni and Sviridenko [SODA 2006]. In both cases, the approximation ratio was in fact shown for a more general version of the problem, for which improving 1 − 1/e is NPhard. In this paper, we show how to improve the 1 − 1/e approximation ratio, both for SMW and for GAP. A common theme in both improvements is the use of a new and optimal Fair Contention Resolution technique....
Uriel Feige, Jan Vondrák
Added 11 Jun 2010
Updated 11 Jun 2010
Type Conference
Year 2006
Where FOCS
Authors Uriel Feige, Jan Vondrák
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