Journal of Combinatorial Theory Series B
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Generalized arc consistency for global cardinality constraint
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Parameterized Complexity
Monadic Second Order Logic on Graphs with Local Cardinality Constraints
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
The parameterized complexity of global constraints
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
The extended global cardinality constraint: An empirical survey
Artificial Intelligence
Hi-index | 0.00 |
We study the consistency problem for extended global cardinality (EGC) constraints. An EGC constraint consists of a set X of variables, a set D of values, a domain D(x) ⊆ D for each variable x, and a "cardinality set" K(d) of non-negative integers for each value d. The problem is to instantiate each variable x with a value in D(x) such that for each value d, the number of variables instantiated with d belongs to the cardinality set K(d). It is known that this problem is NP-complete in general, but solvable in polynomial time if all cardinality sets are intervals. First we pinpoint connections between EGC constraints and general factors in graphs. This allows us to extend the known polynomial-time case to certain non-interval cardinality sets. Second we consider EGC constraints under restrictions in terms of the treewidth of the value graph (the bipartite graph representing variable-value pairs) and the cardinality-width (the largest integer occurring in the cardinality sets). We show that EGC constraints can be solved in polynomial time for instances of bounded treewidth, where the order of the polynomial depends on the treewidth. We show that (subject to the complexity theoretic assumption FPT ≠ W[1]) this dependency cannot be avoided without imposing additional restrictions. If, however, also the cardinality-width is bounded, this dependency gets removed and EGC constraints can be solved in linear time.