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A case study in comparison based complexity: Finding the nearest value(s)

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Algorithms and Data Structures (WADS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 519))

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Abstract

It is shown that 5n/4 plus-minus lower order terms comparisons on average are necessary and sufficient to solve the problem of finding the values of ranks immediately above and below a specified element x in a set X of size n>1. When x turns out to be the median of X, 1.5n+√πn/8+O(lg n) comparisons are proven to be sufficient. n+min(k, n−k)+3 ln n+O(1) comparisons are sufficient if k, the rank of x in X, differs from n/2 by Θ(n).

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References

  1. M. Blum, R.W. Floyd, V.R. Pratt, R.L. Rivest and R.E. Tarjan, Time Bounds for Selection, J. Compt. and Sys. Sci., 7, 1973, pp. 448–461.

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  2. W. Cunto and J.I. Munro, Closest Neighbor Problem, Proceedings 22-nd Allerton Conference, Urbana, Illinois, 1984, pp. 510–515.

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  3. W. Cunto and J.I. Munro, Average Case Selection, JACM, 36, 1989, pp. 270–279.

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  4. R.W. Floyd and R.L. Rivest, Expected Time Bounds for Selection, CACM, 18, 1975, pp. 165–172.

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  5. R.W. Floyd and R.L. Rivest, Algorithm 489: The Algorithm SELECT for Finding the ith Smallest of n elements, CACM, 18, 1975, pp. 173.

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Author information

Authors and Affiliations

  1. Centro Científico IBM de Venezuela, A.P. 64778, Caracas, Venezuela

    Walter Cunto

  2. Department of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ont., Canada

    J. Ian Munro

  3. Departamento de Ciencias de la Computación, Universidad de Chile, Blanco Encalada 2120, Casilla, 2777, Santiago, Chile

    Patricio V. Poblete

Authors
  1. Walter Cunto
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  2. J. Ian Munro
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  3. Patricio V. Poblete
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Editor information

Frank Dehne Jörg-Rüdiger Sack Nicola Santoro

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© 1991 Springer-Verlag Berlin Heidelberg

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Cunto, W., Munro, J.I., Poblete, P.V. (1991). A case study in comparison based complexity: Finding the nearest value(s). In: Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1991. Lecture Notes in Computer Science, vol 519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028244

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  • DOI: https://doi.org/10.1007/BFb0028244

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54343-5

  • Online ISBN: 978-3-540-47566-8

  • eBook Packages: Springer Book Archive

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