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Faster backtracking algorithms for the generation of symmetry-invariant permutations. (English) Zbl 1013.94011

Summary: 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 \(n\), \(19\leq n\leq 24\).

MSC:

94A55 Shift register sequences and sequences over finite alphabets in information and communication theory
05C30 Enumeration in graph theory
68W10 Parallel algorithms in computer science
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