TY - GEN
T1 - Constraints of difference and equality
T2 - 15th International Conference on Principles and Practice of Constraint Programming, CP 2009
AU - Hebrard, Emmanuel
AU - Marx, Dániel
AU - O'Sullivan, Barry
AU - Razgon, Igor
PY - 2009/11/2
Y1 - 2009/11/2
N2 - Many combinatorial problems encountered in practice involve constraints that require that a set of variables take distinct or equal values. The AllDifferent constraint, in particular, ensures that all variables take distinct values. Two soft variants of this constraint were proposed in [4], defined either with respect to a so-called variable or graph-based cost function. When requiring similarity, as opposed to diversity, one can consider the dual definition either for the cost or for the basic constraint itself, that is, AllEqual in our case. Six cost functions can be defined by exploring every combination of these definitions. It is therefore natural to study the complexity of achieving arc consistency and bounds consistency on them. From our earlier work on this topic an open problem remained, namely achieving bounds consistency on the maximisation of the SoftAllDiff constraint when considering the graph-based cost. In this paper we resolve this problem. Therefore, we give a complete taxonomy of constraints of equality and difference, based on the alternative objective functions used for the soft variants.
AB - Many combinatorial problems encountered in practice involve constraints that require that a set of variables take distinct or equal values. The AllDifferent constraint, in particular, ensures that all variables take distinct values. Two soft variants of this constraint were proposed in [4], defined either with respect to a so-called variable or graph-based cost function. When requiring similarity, as opposed to diversity, one can consider the dual definition either for the cost or for the basic constraint itself, that is, AllEqual in our case. Six cost functions can be defined by exploring every combination of these definitions. It is therefore natural to study the complexity of achieving arc consistency and bounds consistency on them. From our earlier work on this topic an open problem remained, namely achieving bounds consistency on the maximisation of the SoftAllDiff constraint when considering the graph-based cost. In this paper we resolve this problem. Therefore, we give a complete taxonomy of constraints of equality and difference, based on the alternative objective functions used for the soft variants.
UR - http://www.scopus.com/inward/record.url?scp=70350381827&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-04244-7_35
DO - 10.1007/978-3-642-04244-7_35
M3 - Conference contribution
AN - SCOPUS:70350381827
SN - 3642042430
SN - 9783642042430
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 424
EP - 438
BT - Principles and Practice of Constraint Programming - CP 2009 - 15th International Conference, CP 2009, Proceedings
Y2 - 20 September 2009 through 24 September 2009
ER -