Abstract
A tree-backtracking-based technique, permutation tree generation with Anterior-items-in-an-array for Remaining Distinct Elements (ARDE), is introduced for multiset and pure permutations. We analyze the algorithm at the assembly level and obtain its time formula for pure permutations. We mathematically prove that our time formula is 11.5% faster than the corresponding formula of the previous fastest algorithm for pure permutations for any length N > 3. We also offer related source codes and executable files on our web site for others to use.
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Chen, R.J., Reschke, K.S., Tong, M.: Code of evaluation and comparison for multiset permutations (2010), http://software.xmu.edu.cn/View/ArticleShow.aspx?aid=3108
Knuth, D.E.: MMIX: A RISC Computer for the New Millennium. In: The Art of Computer Programming. Fascicle, vol. 1. Addison-Wesley, Co., Inc., Reading (2005)
Sedgewick, R.: Permutation generation methods. ACM Computing Surveys (CSUR) 9, 137–164 (1997)
Sedgewick, R.: Permutation generation methods. Dagstuhl Workshop on Data Structures, Wadern, Germany (2002), http://www.cs.princeton.edu/~rs/talks/perms.pdf (accessed March 22, 2009)
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© 2012 Springer-Verlag Berlin Heidelberg
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Chen, R.J., Reschke, K.S., Hu, H. (2012). Design and Analysis of a Tree-Backtracking Algorithm for Multiset and Pure Permutations. In: Arumugam, S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2012. Lecture Notes in Computer Science, vol 7643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35926-2_31
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DOI: https://doi.org/10.1007/978-3-642-35926-2_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35925-5
Online ISBN: 978-3-642-35926-2
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