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The Computer Journal 2000 43(4):290-300; doi:10.1093/comjnl/43.4.290
© 2000 by British Computer Society
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Generating Regular k-ary Trees Efficiently

Limin Xiang1, Kazuo Ushijima1 and Selim G. Akl2

1 Department of Computer Science and Communication Engineering, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan Email: xiang@csce.kyushu-u.ac.jp 2 Department of Computing and Information Science, Queen's University, Kingston, Ontario, Canada K7L 3N6

A recursive algorithm GenWordsR and a non-recursive algorithm GenWordsNR are presented in this paper to generate sequences for regular k-ary trees efficiently. They are compared with some of the previous recursive and non-recursive algorithms for this problem that were found in the literature. When the average number of recursive calls is used as a measure of the time complexity of recursive algorithms for generating k-ary trees, O(k) calls for a k-ary tree is the bestresult in the previous recursive algorithms, while O(1/k) calls for a k-ary tree is needed by GenWordsR. When the average number of comparisons is used as a measure of the time complexity of non-recursive algorithms for generating k-ary trees, GenWordsNR outperforms the previous non-recursive algorithms. As k increases, the number (and the average number) of comparisons performed by GenWordsNR tends to 66% that of the best previous non-recursive algorithms.

Received 30 March, 2000. Revised 24 August, 2000.


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