Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
An incremental linear-time algorithm for recognizing interval graphs
SIAM Journal on Computing
Introduction to algorithms
Computationally Manageable Combinational Auctions
Management Science
An O(n2 algorithm for circular-arc graph recognition
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Constrained multi-object auctions and b-matching
Information Processing Letters
An efficient approximate allocation algorithm for combinatorial auctions
Proceedings of the 3rd ACM conference on Electronic Commerce
Taming the Computational Complexity of Combinatorial Auctions: Optimal and Approximate Approaches
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
An Algorithm for Optimal Winner Determination in Combinatorial Auctions
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on 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
Some Tractable Combinatorial Auctions
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Solving concisely expressed combinatorial auction problems
Eighteenth national conference on Artificial intelligence
BOB: improved winner determination in combinatorial auctions and generalizations
Artificial Intelligence
Combinatorial Auctions: A Survey
INFORMS Journal on Computing
CABOB: a fast optimal algorithm for combinatorial auctions
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 2
Modeling complex multi-issue negotiations using utility graphs
Proceedings of the fourth international joint conference on Autonomous agents and multiagent systems
On the complexity of combinatorial auctions: structured item graphs and hypertree decomposition
Proceedings of the 8th ACM conference on Electronic commerce
Combinatorial auctions with tractable winner determination
ACM SIGecom Exchanges
Properties of tree convex constraints
Artificial Intelligence
Simple randomized algorithms for tractable row and tree convex constraints
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Combinatorial auctions with k-wise dependent valuations
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Computational aspects of mechanism design
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 4
Charting the tractability frontier of mixed multi-unit combinatorial auctions
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
An investigation of representations of combinatorial auctions
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Algorithms and theory of computation handbook
Comparing multiagent systems research in combinatorial auctions and voting
Annals of Mathematics and Artificial Intelligence
Computing optimal outcomes under an expressive representation of settings with externalities
Journal of Computer and System Sciences
A simpler linear-time recognition of circular-arc graphs
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
A REVIEW OF TREE CONVEX SETS TEST
Computational Intelligence
Decomposing combinatorial auctions and set packing problems
Journal of the ACM (JACM)
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Combinatorial auctions (CAs) are important mechanisms for allocating interrelated items. Unfortunately, winner determination is NP-complete unless there is special structure. We study the setting where there is a graph (with some desired property), with the items as vertices, and every bid bids on a connected set of items. Two computational problems arise: 1) clearing the auction when given the item graph, and 2) constructing an item graph (if one exists) with the desired property. 1 was previously solved for the case of a tree or a cycle, and 2 for the case of a line graph or a cycle. We generalize the first result by showing that given an item graph with bounded treewidth, the clearing problem can be solved in polynomial time (and every CA instance has some treewidth; the complexity is exponential in only that parameter). We then give an algorithm for constructing an item tree (treewidth 1) if such a tree exists, thus closing a recognized open problem. We show why this algorithm does not work for treewidth greater than 1, but leave open whether item graphs of (say) treewidth 2 can be constructed in polynomial time. We show that finding the item graph with the fewest edges is NP-complete (even when a graph of treewidth 2 exists). Finally, we study how the results change if a bid is allowed to have more than one connected component. Even for line graphs, we show that clearing is hard even with 2 components, and constructing the line graph is hard even with 5.