An incremental linear-time algorithm for recognizing interval graphs
SIAM Journal on Computing
A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
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
Bidding and allocation in combinatorial auctions
Proceedings of the 2nd ACM conference on Electronic commerce
An efficient approximate allocation algorithm for combinatorial auctions
Proceedings of the 3rd ACM conference on Electronic Commerce
Algorithm for optimal winner determination in combinatorial auctions
Artificial Intelligence
Truth revelation in approximately efficient combinatorial auctions
Journal of the ACM (JACM)
Taming the Computational Complexity of Combinatorial Auctions: Optimal and Approximate Approaches
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
Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width
Journal of Computer and System Sciences - Special issu on PODS 2001
Combinatorial auctions with structured item graphs
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Combinatorial auctions with tractable winner determination
ACM SIGecom Exchanges
Generalized hypertree decompositions: NP-hardness and tractable variants
Journal of the ACM (JACM)
Tractable Optimization Problems through Hypergraph-Based Structural Restrictions
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
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
Constraint optimization problems and bounded tree-width revisited
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
A REVIEW OF TREE CONVEX SETS TEST
Computational Intelligence
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The winner determination problem in combinatorial auctions is the problem of determining the allocation of the items among the bidders that maximizes the sum of the accepted bid prices. While this problem is in general NP-hard, it is known to be feasible in polynomial time on those instances whose associated item graphs have bounded treewidth (called structured item graphs). Formally, an item graph is a graph whose nodes are in one-to-one correspondence with items, and edges are such that for any bid, the items occurring in it induce a connected subgraph. Note that many item graphs might be associated with a given combinatorial auction, depending on the edges selected for guaranteeing the connectedness. In fact, the tractability of determining whether a structured item graph of a fixed treewidth exists (and if so, computing one) was left as a crucial open problem.In this paper, we solve this problem by proving that the existence of a structured item graph is computationally intractable, even for treewidth 3. Motivated by this bad news, we investigate different kinds of structural requirements that can be used to isolate tractable classes of combinatorial auctions. We show that the notion of hypertree decomposition, a recently introduced measure of hypergraph cyclicity, turns out to be most useful here. Indeed, we show that the winner determination problem is solvable in polynomial time on instances whose bidder interactions can be represented with (dual) hypergraphs having bounded hypertree width. Even more surprisingly, we show that the class of tractable instances identified by means of our approach properly contains the class of instances having a structured item graph.