An integer linear program (ILP) is symmetric if its variables can be permuted without
changing the structure of the problem. Areas where symmetric ILPs arise range from applied …

Publisher Summary This chapter reviews that symmetry in constraints has always been
important but in recent years has become a major research area in its own right. A key …

Combinatorial Optimization is an important area of computer science that has many
theoretical and practical applications. In this thesis, we present important contributions to …

Many symmetry breaking techniques assume that the symmetries of a CSP are given as
input in addition to the CSP itself. We present a method that can be used to detect all the …

Many and diverse combinatorial problems have been solved successfully using finite-
domain constraint programming. However, to apply constraint programming to a particular …

We present a new conceptual abstraction in symmetry breaking–the GE-tree. The
construction and traversal of a GE-tree breaks all symmetries in any constraint satisfaction or …

Symmetries in constraint satisfaction problems (CSPs) are one of the difficulties that
practitioners have to deal with. We present in this paper a new method based on the …

Symmetry occurs frequently in Constraint Satisfaction Problems (CSPs). For instance, in 3-
colouring the nodes of a graph, a CSP model that assigns a specific colour to each node has …

We introduce a novel approach for symmetry breaking by dominance detection (SBDD). The
essence of SBDD is to perform 'dominance checks' at each node in a search tree to ensure …

Symmetries in constraint satisfaction problems (CSPs) are one of the difficulties that
practitioners have to deal with. We present in this paper a new method based on the …