Taming the computational complexity of combinatorial auctions: Optimal and approximate approaches

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Taming the computational complexity of combinatorial auctions: Optimal and approximate approaches (1999)

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by Yuzo Fujishima , Kevin Leyton-brown , Yoav Shoham

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@INPROCEEDINGS{Fujishima99tamingthe,
    author = {Yuzo Fujishima and Kevin Leyton-brown and Yoav Shoham},
    title = {Taming the computational complexity of combinatorial auctions: Optimal and approximate approaches},
    booktitle = {},
    year = {1999},
    pages = {548--553}
}

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Abstract

In combinatorial auctions, multiple goods are sold simultaneously and bidders may bid for arbitrary combinations of goods. Determining the outcome of such an auction is an optimization problem that is NP-complete in the general case. We propose two methods of overcoming this apparent intractability. The first method, which is guaranteed to be optimal, reduces running time by structuring the search space so that a modified depth-first search usually avoids even considering allocations that contain conflicting bids. Caching and pruning are also used to speed searching. Our second method is a heuristic, market-based approach. It sets up a virtual multi-round auction in which a virtual agent represents each original bid bundle and places bids, according to a fixed strategy, for each good in that bundle. We show through experiments on synthetic data that (a) our first method finds optimal allocations quickly and offers good anytime performance, and (b) in many cases our second method, despite lacking guarantees regarding optimality or running time, quickly reaches solutions that are nearly optimal. 1 Combinatorial Auctions Auction theory has received increasing attention from computer scientists in recent years. 1 One reason is the explosion of internet-based auctions. The use of auctions in business-to-business trades is also increasing rapidly [Cortese and Stepanek, 1998]. Within AI there is growing interest in using auction mechanisms to solve distributed resource allocation problems. For example, auctions and other market mechanisms are used in network bandwidth allocation, distributed configuration design, factory scheduling, and operating system memory allocation [Clearwater, 1996]. Market-oriented programming has

Keyphrases

combinatorial auction approximate approach computational complexity second method first method multiple good configuration design apparent intractability modified depth-first search market mechanism search space fixed strategy place bid resource allocation problem general case virtual agent market-oriented programming running time factory scheduling network bandwidth allocation original bid bundle synthetic data conflicting bid many case auction mechanism combinatorial auction auction theory computer scientist optimal allocation optimization problem recent year internet-based auction system memory allocation clearwater business-to-business trade virtual multi-round auction arbitrary combination good anytime performance market-based approach

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