Faster backtracking algorithms for the generation of symmetry-invariant permutations

Abstract

A new backtracking algorithm is developed for generating classes of permutations, that are invariant under the group $G_4$ of rigid motions of the square generated by reflections about the horizontal and vertical axes. Special cases give a new algorithm for generating solutions of the classical $n$-queens problem, as well as a new algorithm for generating Costas sequences, which are used in encoding radar and sonar signals. Parallel implementations of this latter algorithm have yielded new Costas sequences for length $n$, $19\le n\le 24$.