In Search of a Better Method to Break Row and Column Symmetries

Complete row and column symmetry breaking in constraint satisfaction problems using the lex leader method is generally prohibitively costly. Double lex, which is derived from lex leader, is commonly used in practice as an incomplete symmetry-breaking method for row and column symmetries. This technique uses a row-wise ordering to construct the lex leader. For this reason, it is generally counterproductive to choose a search ordering that is not also row-wise. It seems logical that the search order should be used to pick the symmetry breaking technique, rather than the other way around. This paper surveys other possible orderings and investigates one particular ordering, snake ordering. From this we derive a corresponding incomplete set of symmetry breaking constraints, snake lex. We present experimental data comparing double lex and the snake lex, showing that snake lex is substantially faster than double lex in many cases.