Inapproximability of Combinatorial Public Projects

  • Authors:
  • Michael Schapira;Yaron Singer

  • Affiliations:
  • The School of Computer Science and Engineering, The Hebrew University of Jerusalem, Israel;Computer Science Division, UC Berkeley, USA

  • Venue:
  • WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
  • Year:
  • 2008

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Abstract

We study the Combinatorial Public Project Problem (CPPP ) in which n agents are assigned a subset of m resources of size k so as to maximize the social welfare. Combinatorial public projects are an abstraction of many resource-assignment problems (Internet-related network design, elections, etc.). It is known that if all agents have submodular valuations then a constant approximation is achievable in polynomial time. However, submodularity is a strong assumption that does not always hold in practice. We show that (unlike similar problems such as combinatorial auctions) even slight relaxations of the submodularity assumption result in non-constant lower bounds for approximation.