A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Fast parallel algorithms for graph matching problems
Fast parallel algorithms for graph matching problems
A fast algorithm for the bound consistency of alldiff constraints
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Approximation algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the Approximation Properties of Independent Set Problem in Degree 3 Graphs
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Faster Algorithms for Bound-Consistency of the Sortedness and the Alldifferent Constraint
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
On the system of two all_different predicates
Information Processing Letters
A fast and simple algorithm for bounds consistency of the all different constraint
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SIAM Journal on Discrete Mathematics
Constraint satisfaction problems: convexity makes all different constraints tractable
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Filtering algorithms for global chance constraints
Artificial Intelligence
Constraint satisfaction problems: Convexity makes AllDifferent constraints tractable
Theoretical Computer Science
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Given a bipartite graph G=(X@?@?D,E@?XxD), an X-perfect matching is a matching in G that covers every node in X. In this paper we study the following generalisation of the X-perfect matching problem, which has applications in constraint programming: Given a bipartite graph as above and a collection F@?2^X of k subsets of X, find a subset M@?E of the edges such that for each C@?F, the edge set M@?(CxD) is a C-perfect matching in G (or report that no such set exists). We show that the decision problem is NP-complete and that the corresponding optimisation problem is in APX when k=O(1) and even APX-complete already for k=2. On the positive side, we show that a 2/(k+1)-approximation can be found in poly(k,|X@?D|) time. We show also that such an approximation M can be found in time (k+(k2)2^k^-^2)poly(|X@?D|), with the further restriction that each vertex in D has degree at most 2 in M.