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Optimal multiway search trees for variable size keys

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This paper considers the construction of optimal search trees for a sequence of n keys of varying sizes, under various cost measures. Constructing optimal search cost multiway trees is NP-hard, although it can be done in pseudo-polynomial time O 3 and space O 2, where L is the page size limit. An optimal space multiway search tree is obtained in O 3 time and O 2 space, while an optimal height tree in O(n 2 log2 n) time and O(n) space both having additionally minimal root sizes. The monotonicity principle does not hold for the above cases. Finding optimal search cost weak B-trees is NP-hard, but a weak B-tree of height 2 and minimal root size can be constructed in O(n log n) time. In addition, if its root is restricted to contain M keys then a different algorithm is applied, having time complexity O(nM log n). The latter solves a problem posed by McCreight.

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References

  1. Bayer, R., McCreight, E.: Organization and maintenance of large ordered indexes. Acta Informat. 1, 173–189 (1971)

    Google Scholar 

  2. Garey, M.R.: Optimal binary search trees with restricted maximal depth. SIAM J. Comput. 2, 101–110 (1974)

    Google Scholar 

  3. Gilbert, E.N., Moore, E.F.: Variable-length binary encodings. Bell System Tech. J. 38, 933–968 (1959)

    Google Scholar 

  4. Gotlieb, L.: Optimal multiway search trees. SIAM J. Comput. 10, 422–433 (1981)

    Google Scholar 

  5. Gotlieb, L., Wood, D.: The construction of optimal multiway search trees and the monotonicity principles. Internat. J. Comput. Math. Sc. A9, 17–24 (1981)

    Google Scholar 

  6. Huddleston, S., Mehlhorn, K.: A new data structure for representing sorted lists: Acta Informat. 17, 157–184 (1982)

    Google Scholar 

  7. Itai, A.: Optimal alphabetic trees. SIAM J. Comput. 5, 9–18 (1976)

    Google Scholar 

  8. Karp, R.M.: Reducibility among combinatorial problems. In: Complexity of Computer Computations. Miller, R.E., Thatcher, J.W. (eds.) New York: Plenum Press 1972

    Google Scholar 

  9. Knuth, D.E.: Optimum binary search trees. Acta Informat. 1, 14–25 (1971)

    Google Scholar 

  10. Knuth, D.E.: The Art of Computer Programming, Vol. 3: Sorting and searching. Reading (Mass.): Addison-Wesley 1973

    Google Scholar 

  11. McCreight, E.M.: Pagination of B*-trees with variable length records. Comm. ACM 20, 670–674 (1977)

    Google Scholar 

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

    Google Scholar 

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  1. Núcleo de Computaç≈o Eletrônica, Universidade Federal do Rio de Janeiro, Caixa Postal 2324, 20.001, Rio de Janeiro - RJ, Brasil

    Jayme Luiz Szwarcfiter

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  1. Jayme Luiz Szwarcfiter
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Luiz Szwarcfiter, J. Optimal multiway search trees for variable size keys. Acta Informatica 21, 47–60 (1984). https://doi.org/10.1007/BF00289139

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  • DOI: https://doi.org/10.1007/BF00289139

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