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Design and Analysis of a Tree-Backtracking Algorithm for Multiset and Pure Permutations

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Combinatorial Algorithms (IWOCA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7643))

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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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References

  1. 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

  2. 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)

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  4. 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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Author information

Authors and Affiliations

  1. Fast Switch, Dublin, OH, USA

    Ray Jinzhu Chen

  2. Department of Computer Science, Stanford University, Stanford, CA, USA

    Kevin Scott Reschke

  3. Software School, Xiamen University, Xiamen, China

    Hailong Hu

Authors
  1. Ray Jinzhu Chen
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  2. Kevin Scott Reschke
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  3. Hailong Hu
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Editor information

Editors and Affiliations

  1. Kalasalingam University, Anand Nagar, 626 126, Krishanakoil, Tamil Nadu, India

    S. Arumugam

  2. Algorithms Research Group, Department of Computing & Software, McMaster University, L8S 4K1, Hamilton, ON, Canada

    W. F. Smyth

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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

  • eBook Packages: Computer ScienceComputer Science (R0)

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