The Submodular Welfare Problem with Demand Queries

: We consider the Submodular Welfare Problem where we have m items and n players with given utility functions wi : 2[m] R+. The utility functions are assumed to be monotone and submodular. We want to find an allocation of disjoint sets of items (S1,S2,...,Sn) maximizing i wi(Si). A (1 - 1/e)-approximation for this problem in the demand oracle model has been given by Dobzinski and Schapira [5]. We improve this algorithm by presenting a (1-1/e+)-approximation for some small fixed > 0. We also show that the Submodular Welfare Problem is NP-hard to approximate within a

• Type: Journal
• Year: 2010
• Where: TOC
• Authors: Uriel Feige, Jan Vondrák
• Keywords: Demand Oracle Model, Management, Submodular Welfare Problem, TOC 2010, Utility Functions