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

  • 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)

Registered author(s):

    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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    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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    1. R. Preston McAfee & John McMillan, 1996. "Analyzing the Airwaves Auction," Journal of Economic Perspectives, American Economic Association, vol. 10(1), pages 159-175, Winter.
    2. ., 2000. "Information costs and the division of labor," Chapters, in: Macroeconomic Instability and Coordination, chapter 14 Edward Elgar Publishing.
    3. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
    4. S.J. Rassenti & V.L. Smith & R.L. Bulfin, 1982. "A Combinatorial Auction Mechanism for Airport Time Slot Allocation," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 402-417, Autumn.
    5. Atamturk, Alper & Nemhauser, George L. & Savelsbergh, Martin W. P., 2000. "Conflict graphs in solving integer programming problems," European Journal of Operational Research, Elsevier, vol. 121(1), pages 40-55, February.
    6. John McMillan, 1994. "Selling Spectrum Rights," Journal of Economic Perspectives, American Economic Association, vol. 8(3), pages 145-162, Summer.
    7. Michael H. Rothkopf & Aleksandar Peke\v{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
    8. Frank Kelly & Richard Steinberg, 2000. "A Combinatorial Auction with Multiple Winners for Universal Service," Management Science, INFORMS, vol. 46(4), pages 586-596, April.
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