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An Experimental Study of Unranking Algorithms

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Experimental and Efficient Algorithms (WEA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3059))

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Abstract

We describe in this extended abstract the experiments that we have conducted in order to fullfil the following goals: a) to obtain a working implementation of the unranking algorithms that we have presented in previous works; b) to assess the validity and range of application of our theoretical analysis of the performance of these algorithms; c) to provide preliminary figures on the practical performance of these algorithms under a reasonable environment; and finally, d) to compare these algorithms with the algorithms for random generation. Additionally, the experiments support our conjecture that the average complexity of boustrophedonic unranking is Θ(nlog n) for many combinatorial classes (namely, those whose specification requires recursion) and that it performs only slightly worse than lexicographic unranking for iterative classes (those which do not require recursion to be specified).

This research was supported by the Future and Emergent Technologies programme of the EU under contract IST-1999-14186 (ALCOM-FT) and the Spanish “Ministerio de Ciencia y Tecnología” programme TIC2002-00190 (AEDRI II).

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References

  1. Nievergelt, J., Reingold, E.M., Deo, N.: Combinatorial Algorithms: Theory and Practice. Prentice-Hall, Englewood Cliffs (1977)

    MATH  Google Scholar 

  2. Even, S.: Combinatorial Algorithms. MacMillan, New York (1973)

    Google Scholar 

  3. Flajolet, P., Salvy, B.: Computer algebra libraries for combinatorial structures. J. Symbolic Comp (also INRIA, num. 2497) 20, 653–671 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  4. Flajolet, P., Sedgewick, R.: The average case analysis of algorithms: Counting and generating functions. Technical Report 1888, INRIA (April 1993)

    Google Scholar 

  5. Flajolet, P., Vitter, J.S.: Average-case Analysis of Algorithms and Data Structures. In: Van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, ch. 9, North-Holland, Amsterdam (1990)

    Google Scholar 

  6. Flajolet, P., Zimmermann, P., Van Cutsem, B.: A calculus for the random generation of combinatorial structures. Theor. Comp. Sci. 132(1), 1–35 (1994)

    Article  MATH  Google Scholar 

  7. Kreher, D.L., Stinson, D.R.: Combinatorial Algorithms: Generation, Enumeration and Search. CRC Press LLC, Boca Raton (1999)

    MATH  Google Scholar 

  8. Liebehenschel, J.: Ranking and unranking of lexicographically ordered words: An average-case analysis. Journal of Automata, Languages and Combinatorics 2(4), 227–268 (1997)

    MATH  MathSciNet  Google Scholar 

  9. Liebehenschel, J.: Ranking and unranking of a generalized dyck language and the application to the generation of random trees. In: The Fifth International Seminar on the Mathematical Analysis of Algorithms, Bellaterra, Spain (June 1999)

    Google Scholar 

  10. Martínez, C., Molinero, X.: Unranking of labelled combinatorial structures. In: Krob, D., Mikhalev, A.A., Mikhalev, A.V. (eds.) Formal Power Series and Algebraic Combinatorics: 12th International Conference; Procedings / FPSAC 2000, June 2000, pp. 288–299. Springer, Heidelberg (2000)

    Google Scholar 

  11. Martínez, C., Molinero, X.: A generic approach for the unranking of labeled combinatorial classes. Random Structures & Algorithms 19(3-4), 472–497 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Martínez, C., Molinero, X.: Generic algorithms for the generation of combinatorial objects. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 572–581. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  13. Nijenhuis, A., Wilf, H.S.: Combinatorial Algorithms: For Computers and Calculators. Academic Press, Inc., London (1978)

    MATH  Google Scholar 

  14. Pallo, J.M.: Enumerating, ranking and unranking binary trees. The Computer Journal 29(2), 171–175 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  15. Wilf, H.S.: East side, west side.. an introduction to combinatorial families-with maple programming (February 1999)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, E-08034, Barcelona, Spain

    Conrado Martínez & Xavier Molinero

Authors
  1. Conrado Martínez
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  2. Xavier Molinero
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Universidade Federal Fluminense, Rua Passo da Pátria, 156, Bloco E, RJ 24210-240, Niterói, Brazil

    Celso C. Ribeiro

  2. Departamento de Ciência da Computação, Universidade Federal Fluminense, Niterói, RJ, Brazil

    Simone L. Martins

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Martínez, C., Molinero, X. (2004). An Experimental Study of Unranking Algorithms. In: Ribeiro, C.C., Martins, S.L. (eds) Experimental and Efficient Algorithms. WEA 2004. Lecture Notes in Computer Science, vol 3059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24838-5_25

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  • DOI: https://doi.org/10.1007/978-3-540-24838-5_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22067-1

  • Online ISBN: 978-3-540-24838-5

  • eBook Packages: Springer Book Archive

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