Global constraints for integer and set value precedence

Abstract

The paper introduces value precedence on integer and set sequences. A useful application of the notion is in breaking symmetries of indistinguishable values, an important class of symmetries in practice. Although value precedence can be expressed straightforwardly using if-then constraints in existing constraint programming systems, the resulting formulation is inefficient both in terms of size and runtime. We present two propagation algorithms for implementing global constraints on value precedence in the integer and set domains. Besides conducting experiments to verify the feasibility and efficiency of our proposal, we characterize also the propagation level attained by various usages of the global constraints as well as the conditions when the constraints can be used consistently with other types of symmetry breaking constraints. © Springer-Verlag Berlin Heidelberg 2004.