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Trans-dichotomous algorithms without multiplication — some upper and lower bounds

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Book cover Algorithms and Data Structures (WADS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1272))

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Abstract

We show that on a RAM with addition, subtraction, bitwise Boolean operations and shifts, but no multiplication, there is a transdichotomous solution to the static dictionary problem using linear space and with query time √log n(log log n)1+0(1). On the way, we show that two w-bit words can be multiplied in time (log w)1+0(1) and that time μ(log w) is necessary, and that θ(log log w) time is necessary and sufficient for identifying the least significant set bit of a word.

Some of the results of this paper appeared in the PhD thesis of this author

Supported by the ESPRIT Long Term Research Programme of the EU under project number 20244 (ALCOM-IT). Part of this work was done while the author was at the University of Toronto.

This research was supported by a grant from the Natural Science and Engineering Council of Canada.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia and Luleå University, Luleå, Sweden

    Andrej Brodnik

  2. BRICS, Centre of the Danish National Research Foundation, University of Aarhus, Denmark

    Peter Bro Miltersen

  3. Department of Computer Science, University of Waterloo, Canada

    J. Ian Munro

Authors
  1. Andrej Brodnik
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  2. Peter Bro Miltersen
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  3. J. Ian Munro
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Editor information

Frank Dehne Andrew Rau-Chaplin Jörg-Rüdiger Sack Roberto Tamassia

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© 1997 Springer-Verlag Berlin Heidelberg

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Brodnik, A., Miltersen, P.B., Munro, J.I. (1997). Trans-dichotomous algorithms without multiplication — some upper and lower bounds. In: Dehne, F., Rau-Chaplin, A., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 1997. Lecture Notes in Computer Science, vol 1272. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63307-3_80

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  • DOI: https://doi.org/10.1007/3-540-63307-3_80

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63307-5

  • Online ISBN: 978-3-540-69422-9

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