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Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
A comparison of structural CSP decomposition methods
Artificial Intelligence
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ICTAI '08 Proceedings of the 2008 20th IEEE International Conference on Tools with Artificial Intelligence - Volume 01
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ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
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AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Tractable hypergraph properties for constraint satisfaction and conjunctive queries
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NGITS'06 Proceedings of the 6th international conference on Next Generation Information Technologies and Systems
Tractable counting of the answers to conjunctive queries
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Annals of Mathematics and Artificial Intelligence
Decomposing combinatorial auctions and set packing problems
Journal of the ACM (JACM)
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modeling those scenarios where solutions are associated with costs. Within these frameworks, computing an optimal solution (short: MIN problem), enumerating the best K solutions (Top-K), and computing the next solution following one that is given at hand (NEXT) are all NP-hard problems. In fact, only some restricted islands of tractability for them have been singled out in the literature. The paper fills the gap, by studying the complexity of MIN, TOP-K, and Next over classes of acyclic and nearly acyclic instances, as they can be identified via structural decomposition methods. The analysis is provided for both monotone cost-functions and non-monotone ones (which have been largely ignored so far). Also, multicriteria optimization is considered, as instances may have a number of cost functions to be minimized together, according to a given precedence relationship. Large islands of tractability are identified and, for classes of bounded-arity instances, the tractability frontier of constraint optimization is precisely charted.