Proceedings ArticleDOI
An efficient approximate allocation algorithm for combinatorial auctions
Edo Zurel,Noam Nisan +1 more
- pp 125-136
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This work proposes a heuristic for allocation in combinatorial auctions that can provide excellent solutions for problems with over 1000 items and 10,000 bids and achieves an average approximation error of less than 1%.Abstract:
We propose a heuristic for allocation in combinatorial auctions. We first run an approximation algorithm on the linear programming relaxation of the combinatorial auction. We then run a sequence of greedy algorithms, starting with the order on the bids determined by the approximate linear program and continuing in a hill-climbing fashion using local improvements in the order of bids. We have implemented the algorithm and have tested it on the complete corpus of instances provided by Vohra and de Vries as well as on instances drawn from the distributions of Leyton-Brown, Pearson, and Shoham. Our algorithm typically runs two to three orders of magnitude faster than the reported running times of Vohra and de Vries, while achieving an average approximation error of less than 1%. This algorithm can provide, in less than a minute of CPU time, excellent solutions for problems with over 1000 items and 10,000 bids. We thus believe that combinatorial auctions for most purposes face no practical computational hurdles.read more
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References
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Journal ArticleDOI
Combinatorial Auctions: A Survey
Sven de Vries,Rakesh Vohra +1 more
TL;DR: The state of knowledge about the design of combinatorial auctions is surveyed and some new insights are presented.
Journal ArticleDOI
Computationally Manageable Combinational Auctions
TL;DR: In this paper, the problem of determining the revenue maximizing set of nonconflicting bids can be solved for combinational auctions where the value of assets to a bidder depends on which other assets he or she wins.
Proceedings ArticleDOI
Bidding and allocation in combinatorial auctions
TL;DR: It is proved that the LP approach is an optimal allocation if and only if prices can be attached to single items in the auction, and suggests greedy and branch-andbound heuristics based on LP for other cases.
Journal ArticleDOI
Fast approximation algorithms for fractional packing and covering problems
TL;DR: The techniques developed in this paper greatly outperform the general methods in many applications, and are extensions of a method previously applied to find approximate solutions to multicommodity flow problems.
Proceedings Article
Taming the Computational Complexity of Combinatorial Auctions: Optimal and Approximate Approaches
TL;DR: This work proposes two methods of overcoming apparent intractability in combinatorial auctions by structuring the search space so that a modified depth-first search usually avoids even considering allocations that contain conflicting bids.