Skip to main content
SpringerLink
Log in
Book cover

International Symposium on Mathematical Foundations of Computer Science

MFCS 1995: Mathematical Foundations of Computer Science 1995 pp 211–220Cite as

Asymptotically efficient in-place merging

  • Contributed Papers
  • Conference paper
  • First Online:

  • 940 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 969))

Abstract

Two new linear-time algorithms for in-place merging are presented. Both algorithms perform at most (1 + t)m + n/2 2 + o(m) element comparisons, where m and n are the sizes of the input sequences, m ⩽ n, and t = ILlog 2(n/m)⌋. The first algorithm is for unstable merging and it carries out no more than 4(m + n) + o(n) element moves. The second algorithm is for stable merging and it accomplishes at most 15m + 13n + o(n) moves.

Financially supported by the Graduate School of Turku Centre for Computer Science.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dudziński K., Dydek A., “On stable minimum storage merging algorithm”, Information Processing Letters 12 (1981) 5–8

    Google Scholar 

  2. Dvořák S., Ďurian B., “Towards an efficient merging”, Proc. of the 12th Symposium on Mathematical Foundations of Computer Science (1986) 290–298

    Google Scholar 

  3. Huang B-C., Langston M. A., “Practical in-place merging”, Communications of the ACM 31 (1988) 348–352

    Article  Google Scholar 

  4. Huang B-C., Langston M. A., “Fast stable merging and sorting in constant extra space”, Proc. of the 1st International Conference on Computing and Information (1989) 71–79

    Google Scholar 

  5. Hwang F. K., Lin S., “A simple algorithm for merging two disjoint linearly ordered sets”, SIAM Journal on Computing 1 (1972) 31–39

    Google Scholar 

  6. Katajainen J., Pasanen T., Teuhola J., “Practical in-place mergesort”, TR 94/1, Department of Computer Science, University of Copenhagen, Denmark (1994)

    Google Scholar 

  7. Knuth D. E., The Art of Computer Programming Vol. 3: Sorting and Searching, 2nd Printing, Addison-Wesley (1975)

    Google Scholar 

  8. Kronrod M. A., “Optimal ordering algorithm without operational field”, Soviet Math. Dokl. 10 (1969) 744–746

    Google Scholar 

  9. Mannila H., Ukkonen E., “A simple linear-time algorithm for in situ merging”, Information Processing Letters 18 (1984) 203–208

    MathSciNet  Google Scholar 

  10. Munro J. I., Raman V., “Sorting with minimum data movement”, Journal of Algorithms 13 (1992) 374–393

    Google Scholar 

  11. Pardo L. T., “Stable sorting and merging with optimal space and time bounds”, SIAM Journal on Computing 6 (1977) 351–372

    Google Scholar 

  12. Pasanen T., “Lajittelu minimitilassa”, M.Sc. Thesis T-93-3, Department of Computer Science, University of Turku, Finland (1993)

    Google Scholar 

  13. Raman V., “Sorting in-place with minimum data movement”, Ph.D. Thesis CS-91-12, Computer Science Department, University of Waterloo, Ontario (1991)

    Google Scholar 

  14. Salowe J. S., Steiger W. L., “Simplified stable merging tasks”, Journal of Algorithms 8 (1987) 557–571

    Google Scholar 

  15. Symvonis A., “Optimal Stable Merging”, Proc. of the 6th International Conference on Computing and Information (1994) 124–143

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Copenhagen, Universitetsparken 1, DK-2100, Copenhagen East, Denmark

    Jyrki Katajainen & George Titan

  2. Department of Computer Science, University of Turku, Lemminkäisenkatu 14 A, FIN-20520, Turku, Finland

    Tomi Pasanen

Authors
  1. Jyrki Katajainen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tomi Pasanen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. George Titan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jiří Wiedermann Petr Hájek

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Katajainen, J., Pasanen, T., Titan, G. (1995). Asymptotically efficient in-place merging. In: Wiedermann, J., Hájek, P. (eds) Mathematical Foundations of Computer Science 1995. MFCS 1995. Lecture Notes in Computer Science, vol 969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60246-1_127

Download citation

  • DOI: https://doi.org/10.1007/3-540-60246-1_127

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60246-0

  • Online ISBN: 978-3-540-44768-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation