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Optimization problems arising from the incorporation of split values in search trees

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Combinatorial Optimization II

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 13))

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Abstract

A review of techniques for the construction of optimal binary search trees leads to a new algorithm for the construction of nearly optimal split trees. Results are given to compare the efficiency of such trees with that of median split trees and some open problems arising are discussed. The concept of a generalised tree is introduced together with a description of how the solution of the difficult problems arising would have a considerable practical impact in the design of data bases.

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References

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

    Article  Google Scholar 

  2. J. Bruno and E.G. Coffman, “Nearly optimal binary search trees”, Proceedings of IFIP Conference, Ljublyana, Yugoslavia (North-Holland, Amsterdam, 1972).

    Google Scholar 

  3. D. Comer, “The ubiquitous B-tree”, Computing Surveys 11 (1979) 121–137.

    Article  MATH  Google Scholar 

  4. M.L. Fredman, “Two applications of a probabilistic search technique: sorting x+y and building balanced search trees”, Proceedings of the 7th Association for Computing Machinery Symposium on the Theory of Computing, Albuquerque (1975).

    Google Scholar 

  5. H.F. Gaines, Cryptanalysis (Dover, New York, 1956).

    Google Scholar 

  6. T.C. Hu, “Some results and problems in binary trees”, in: R. Rustin, ed., Combinatorial algorithms (Academic Press, New York, 1972) pp. 11–15.

    Google Scholar 

  7. T.C. Hu and A.C. Tucker, “Optimal computer search trees and variable-length alphabetic codes”, Journal of the Society of Industrial and Applied Mathematics on Applied Mathematics (1971) 514–532.

    Google Scholar 

  8. D.E. Knuth, “Optimum binary search trees”, Acta Informatica 1 (1971) 14–25.

    Article  MATH  Google Scholar 

  9. D.E. Knuth, The art of computer programming. Volume 1: fundamental algorithms (Addison-Wesley, Reading, MA, 1968).

    Google Scholar 

  10. D.E. Knuth, The art of computer programming. Volume 3: sorting and searching (Addison-Wesley, Reading, MA, 1973).

    Google Scholar 

  11. K. Melhorn, “Nearly optimal binary search trees”, Acta Informatica 5 (1975) 287–295.

    Google Scholar 

  12. B.A. Shiel, “Median Split trees: a fast look-up technique for frequently occurring keys”, Communications of the Association for Computing Machinery 11 (1978) 947–958.

    Google Scholar 

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V. J. Rayward-Smith

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© 1980 The Mathematical Programming Society

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Rayward-Smith, V.J. (1980). Optimization problems arising from the incorporation of split values in search trees. In: Rayward-Smith, V.J. (eds) Combinatorial Optimization II. Mathematical Programming Studies, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120912

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  • DOI: https://doi.org/10.1007/BFb0120912

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00803-0

  • Online ISBN: 978-3-642-00804-7

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