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Finding extrema with unary predicates

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Abstract

We consider the problem of determining the maximum and minimum elements of a setX={x1...,x n }, drawn from some finite universeU of real numbers, using only unary predicates of the inputs. It is shown that θ(n+ log¦U¦) unary predicate evaluations are necessary and sufficient, in the worst case. Results are applied to (i) the problem of determining approximate extrema of a set of real numbers, in the same model, and (ii) the multiparty broadcast communication complexity of determining the extrema of an arbitrary set of numbers held by distinct processors.

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Authors and Affiliations

  1. Department of Computer Science, University of British Columbia, V6T 1W5, Vancouver, BC, Canada

    Feng Gao & David G. Kirkpatrick

  2. Laboratory for Computer Science, MIT, 02139, Cambridge, MA, USA

    Leonidas J. Guibas

  3. DEC Systems Research Center, 130 Lytton Avenue, 94301, Palo Alto, CA, USA

    Leonidas J. Guibas & James Sake

  4. Metaphor Computer Systems, 1965 Charleston Road, 94043, Mountainview, CA, USA

    William T. Laaser

Authors
  1. Feng Gao
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  2. Leonidas J. Guibas
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  3. David G. Kirkpatrick
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  4. William T. Laaser
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  5. James Sake
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Additional information

Communicated by Takao Asano.

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Gao, F., Guibas, L.J., Kirkpatrick, D.G. et al. Finding extrema with unary predicates. Algorithmica 9, 591–600 (1993). https://doi.org/10.1007/BF01190157

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  • DOI: https://doi.org/10.1007/BF01190157

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