Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
The hardness of approximation: gap location
Computational Complexity
Computationally Manageable Combinational Auctions
Management Science
iBundle: an efficient ascending price bundle auction
Proceedings of the 1st ACM conference on Electronic commerce
Bidding and allocation in combinatorial auctions
Proceedings of the 2nd ACM conference on Electronic commerce
Algorithm for optimal winner determination in combinatorial auctions
Artificial Intelligence
Solving Combinatorial Auctions Using Stochastic Local Search
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
An Algorithm for Multi-Unit Combinatorial Auctions
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Accelerating vickrey payment computation in combinatorial auctions for an airline alliance
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
An exact algorithm for IP column generation
Operations Research Letters
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In a combinatorial auction, multiple items are for sale simultaneously to a set of buyers. These buyers are allowed to place bids on subsets of the available items. A special kind of combinatorial auction is the so-called matrix bid auction, which was developed by Day (2004). The matrix bid auction imposes restrictions on what a bidder can bid for a subsets of the items. This paper focusses on the winner determination problem, i.e. deciding which bidders should get what items. The winner determination problem of a general combinatorial auction is NPhard and inapproximable. We discuss the computational complexity of the winner determination problem for a special case of the matrix bid auction. We compare two mathematical programming formulations for the general matrix bid auction winner determination problem. Based on one of these formulations, we develop two branch-and-price algorithms to solve the winner determination problem. Finally, we present computational results for these algorithms and compare them with results from a branch-and-cut approach based on Day and Raghavan (2006).