On the Configuration LP for Maximum Budgeted Allocation

  • Christos Kalaitzis
  • Aleksander Mądry
  • Alantha Newman
  • Lukáš Poláček
  • Ola Svensson
Conference paper

DOI: 10.1007/978-3-319-07557-0_28

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8494)
Cite this paper as:
Kalaitzis C., Mądry A., Newman A., Poláček L., Svensson O. (2014) On the Configuration LP for Maximum Budgeted Allocation. In: Lee J., Vygen J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2014. Lecture Notes in Computer Science, vol 8494. Springer, Cham

Abstract

We study the Maximum Budgeted Allocation problem, i.e., the problem of selling a set of m indivisible goods to n players, each with a separate budget, such that we maximize the collected revenue. Since the natural assignment LP is known to have an integrality gap of \(\frac{3}{4}\), which matches the best known approximation algorithms, our main focus is to improve our understanding of the stronger configuration LP relaxation. In this direction, we prove that the integrality gap of the configuration LP is strictly better than \(\frac{3}{4}\), and provide corresponding polynomial time roundings, in the following restrictions of the problem: (i) the Restricted Budgeted Allocation problem, in which all the players have the same budget and every item has the same value for any player it can be sold to, and (ii) the graph MBA problem, in which an item can be assigned to at most 2 players. Finally, we improve the best known upper bound on the integrality gap for the general case from \(\frac{5}{6}\) to \(2\sqrt{2}-2\approx 0.828\) and also prove hardness of approximation results for both cases.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Christos Kalaitzis
    • 1
  • Aleksander Mądry
    • 1
  • Alantha Newman
    • 1
  • Lukáš Poláček
    • 2
  • Ola Svensson
    • 1
  1. 1.EPFLSwitzerland
  2. 2.KTH Royal Institute of TechnologySweden

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