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CABOB: A Fast Optimal Algorithm for Winner Determination in Combinatorial Auctions

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Author Info

  • Tuomas Sandholm

    ()
    (Computer Science Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • Subhash Suri

    ()
    (Department of Computer Science, University of California, Santa Barbara, California 93106)

  • Andrew Gilpin

    ()
    (CombineNet, Inc., Fifteen 27th Street, Pittsburgh, Pennsylvania 15222)

  • David Levine

    ()
    (CombineNet, Inc., Fifteen 27th Street, Pittsburgh, Pennsylvania 15222)

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    Abstract

    Combinatorial auctions where bidders can bid on bundles of items can lead to more economically efficient allocations, but determining the winners is \scr{N}\scr{P}-complete and inapproximable. We present CABOB, a sophisticated optimal search algorithm for the problem. It uses decomposition techniques, upper and lower bounding (also across components), elaborate and dynamically chosen bid-ordering heuristics, and a host of structural observations. CABOB attempts to capture structure in any instance without making assumptions about the instance distribution. Experiments against the fastest prior algorithm, CPLEX 8.0, show that CABOB is often faster, seldom drastically slower, and in many cases drastically faster---especially in cases with structure. CABOB's search runs in linear space and has significantly better anytime performance than CPLEX. We also uncover interesting aspects of the problem itself. First, problems with short bids, which were hard for the first generation of specialized algorithms, are easy. Second, almost all of the CATS distributions are easy, and the run time is virtually unaffected by the number of goods. Third, we test several random restart strategies, showing that they do not help on this problem---the run-time distribution does not have a heavy tail.

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    File URL: http://dx.doi.org/10.1287/mnsc.1040.0336
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 51 (2005)
    Issue (Month): 3 (March)
    Pages: 374-390

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    Handle: RePEc:inm:ormnsc:v:51:y:2005:i:3:p:374-390

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    Related research

    Keywords: auction; combinatorial auction; winner determination; winner-determination algorithm; search; branch and bound; MIP; anytime algorithm; branching heuristics; dynamically chosen heuristic; bounding across components; random restart;

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    Cited by:
    1. Mu'alem, Ahuva & Nisan, Noam, 2008. "Truthful approximation mechanisms for restricted combinatorial auctions," Games and Economic Behavior, Elsevier, vol. 64(2), pages 612-631, November.
    2. Drexl, Andreas & J├Ârnsten, Kurt & Knof, Diether, 2005. "Non-linear anonymous pricing in combinatorial auctions," Discussion Papers 2005/6, Department of Business and Management Science, Norwegian School of Economics.
    3. Chang, Tsung-Sheng, 2009. "Decision support for truckload carriers in one-shot combinatorial auctions," Transportation Research Part B: Methodological, Elsevier, vol. 43(5), pages 522-541, June.

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