Journal of Applied Mathematics
Volume 2 (2002), Issue 6, Pages 277-287

Faster backtracking algorithms for the generation of symmetry-invariant permutations

Oscar Moreno,1 John Ramírez,2 Dorothy Bollman,3 and Edusmildo Orozco3

1Department of Mathematics and Computer Science, University of Puerto Rico, Rio Piedras 00931-3355, PR, USA
2The Graduate School and University Center, The City University of New York, 365 Fifth Avenue, New York 10016-4309, NY, USA
3Department of Mathematics, University of Puerto Rico, Mayaguez 00681-9018, PR, USA

Received 5 March 2002

Copyright © 2002 Oscar Moreno et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new backtracking algorithm is developed for generating classes of permutations, that are invariant under the group G4 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, 19n24.