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Efficient Construction of Near-Optimal Binary and Multiway Search Trees

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Algorithms and Data Structures (WADS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5664))

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Abstract

We present a new linear-time algorithm for constructing multiway search trees with near-optimal search cost whose running time is independent of the size of the node in the tree. With the analysis of our construction method, we provide a new upper bound on the average search cost for multiway search trees that nearly matches the lower bound. In fact, it is tight for infinitely many probability distributions. This problem is well-studied in the literature for the case of binary search trees. Using our new construction method, we are able to provide the tightest upper bound on the average search cost for an optimal binary search tree.

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References

  1. Bayer, R., McCreight, E.M.: Organization and maintenance of large ordered indexes. Acta Informatica 1(3), 173–189 (1972)

    Article  MATH  Google Scholar 

  2. Becker, P.: A new algorithm for the construction of optimal B-trees. Nordic Journal of Computing 1, 389–401 (1994)

    MathSciNet  MATH  Google Scholar 

  3. Becker, P.: Construction of nearly optimal multiway trees. In: Jiang, T., Lee, D.T. (eds.) COCOON 1997. LNCS, vol. 1276, pp. 294–303. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  4. Bent, S., Sleator, D., Tarjan, R.: Biased 2-3 trees. In: Annual Symposium on Foundations of Computer Science, pp. 248–254 (1980)

    Google Scholar 

  5. Bent, S., Sleator, D., Tarjan, R.: Biased search trees. SIAM J. Comput. 14(3), 545–568 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  6. Feigenbaum, J., Tarjan, R.: Two new kinds of biased search trees. Bell Syst. Tech. J. 62, 3139–3158 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  7. Garsia, A.M., Wachs, M.L.: A new algorithm for minimum cost binary trees. SIAM Journal on Computing 6, 622–642 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gotlieb, L.: Optimal multi-way search trees. SIAM Journal of Computing 10(3), 422–433 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hu, T.C., Tucker, A.C.: Optimal computer search trees and variable-length alphabetical codes. SIAM Journal on Applied Mathematics 21(4), 514–532 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  10. Knuth, D.: The Art of Computer Programming: Sorting and Searching, vol. 3. Addison-Wesley, Reading (1973)

    MATH  Google Scholar 

  11. Knuth, D.: Optimum binary search trees. Acta Informatica 1, 79–110 (1971)

    Article  MATH  Google Scholar 

  12. Mehlhorn, K.: Data structures and algorithms: Sorting und Searching. EATCS Monographs on Theoretical Computer Science, vol. 1. Springer, Berlin (1984)

    MATH  Google Scholar 

  13. Mehlhorn, K.: Nearly optimal binary search trees. Acta Inf. 5, 287–295 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  14. Mehlhorn, K.: A best possible bound for the weighted path length of binary search trees. SIAM Journal on Computing 6, 235–239 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  15. Prisco, R.D., Santis, A.D.: On binary search trees. Information Processing Letters 45(5), 249–253 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  16. Prisco, R.D., Santis, A.D.: New lower bounds on the cost of binary search trees. Theor. Comput. Sci. 156(1&2), 315–325 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  17. Shannon, C.: A mathematical theory of communication. Bell System Technical Journal 27, 379–423, 623–656 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  18. Vaishnavi, V.K., Kriegel, H.P., Wood, D.: Optimum multiway search trees. Acta Informatica 14(2), 119–133 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  19. Yeung, R.: Alphabetic codes revisited. IEEE Transactions on Information Theory 37(3), 564–572 (1991)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Computer Science, Carleton University, Herzberg Building 1125 Colonel By Drive, Ottawa, Ontario, K1S 5B6, Canada

    Prosenjit Bose & Karim Douïeb

Authors
  1. Prosenjit Bose
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  2. Karim Douïeb
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Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina Gavrilova

  3. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, P.O. Box, K1S 5B6, Ontario, Canada

    Jörg-Rüdiger Sack

  4. University of Calgary, Calgary, AB, Canada

    Csaba D. Tóth

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© 2009 Springer-Verlag Berlin Heidelberg

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Bose, P., Douïeb, K. (2009). Efficient Construction of Near-Optimal Binary and Multiway Search Trees. In: Dehne, F., Gavrilova, M., Sack, JR., Tóth , C.D. (eds) Algorithms and Data Structures. WADS 2009. Lecture Notes in Computer Science, vol 5664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03367-4_21

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  • DOI: https://doi.org/10.1007/978-3-642-03367-4_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03366-7

  • Online ISBN: 978-3-642-03367-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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