Skip to main content

A tight lower bound for selection in sorted X+Y

  • Algorithms And Complexity
  • Conference paper
  • First Online:
Advances in Computing and Information — ICCI '91 (ICCI 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 497))

Included in the following conference series:

  • 131 Accesses

Abstract

The complexity of the problem of selecting the k-th element of a sorted matrix is known. In this note we show a lower bound for such a problem in sorted X+Y. This lower bound is tight since the upper bound for sorted matrices holds for sorted X+Y.

On leave from the University of Sao Paulo, Brazil. Member of the BID/USP project.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Blum, R.W. Floyd, V. Pratt, R.L. Rivest and R.E. Tarjan, "Time bounds for selection", JCSS, 7 (1973), pp 448–461

    Google Scholar 

  2. M. Cosnard, J. Duprat and A.G. Ferreira, "The complexity of searching in X + Y and other multisets", Information Processing Letters, 34 (1990) 103–109

    Article  Google Scholar 

  3. M.L.Fredman, "Two applications of a probabilistic search technique: sorting X + Y and building balanced search trees", in Proc. 7-th Annual ACM Symp. on Theory of Computing, (May 1975), ACM, 1975, pp 240–244

    Google Scholar 

  4. G.N. Frederickson and D.B. Johnson, "The complexity of selection and ranking in X + Y and matrices with sorted columns", JCSS 24 (1982), pp 197–208

    Google Scholar 

  5. G.N. Frederickson and D.B. Johnson, "Generalized selection and ranking: sorted matrices", SIAM J. Comput. 13 (1), Feb 1984, pp 197–208

    Article  Google Scholar 

  6. L.H. Harper, T.H. Payne, J.E. Savage and E. Straus, "Sorting X + Y", Comm. ACM 18 (6) (1975), pp 347–349

    Article  Google Scholar 

  7. J.L.Lambert, Sorting the elements of X+Y with O(n2) comparisons, in Proceedings of STACS 90, Feb. 1990, Rouens, France

    Google Scholar 

  8. N. Linial and M. Saks, "Searching ordered structures", Journal of Algorithms 6 (1985), pp 86–103

    Article  Google Scholar 

  9. A. Mirzaian and E. Arjomandi, "Selection in X + Y and matrices with sorted rows and columns", Inf. Proc. Letters 20 (1985), pp 13–17

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Frank Dehne Frantisek Fiala Waldemar W. Koczkodaj

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cosnard, M., Ferreira, A.G. (1991). A tight lower bound for selection in sorted X+Y. In: Dehne, F., Fiala, F., Koczkodaj, W.W. (eds) Advances in Computing and Information — ICCI '91. ICCI 1991. Lecture Notes in Computer Science, vol 497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54029-6_162

Download citation

  • DOI: https://doi.org/10.1007/3-540-54029-6_162

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54029-8

  • Online ISBN: 978-3-540-47359-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics