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A lower bound on the area of permutation layouts

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Abstract

In this paper we prove a tight Ω(n 3) lower bound on the area of rectilinear grids which allow a permutation layout ofn inputs andn outputs. Previously, the best lower bound for the area of permutation layouts with arbitrary placement of the inputs and outputs was Ω(n 2), though Cutler and Shiloach [CS] proved an Ω(n 2.5) lower bound for permutation layouts in which the set of inputs and the set of outputs each lie on horizontal lines. Our lower bound also holds for permutation layouts in multilayer grids as long as a fixed fraction of the paths do not change layers.

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Author notes

  1. Maria Klawe

    Present address: Department of Computer Science, University of British Columbia, V6T 1W5, Vancouver, BC, Canada

Authors and Affiliations

  1. IBM T. J. Watson Research Center, P.O. Box 218, 10598, Yorktown Heights, NY, USA

    Alok Aggarwal

  2. IBM Almaden Research Center, 650 Harry Road, 95120-6099, San Jose, CA, USA

    Maria Klawe

  3. Yale University, New Haven, Connecticut, USA

    David Lichtenstein

  4. Hebrew University of Jerusalem, Jerusalem, Israel

    Nathan Linial & Avi Wigderson

Authors
  1. Alok Aggarwal
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  2. Maria Klawe
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  3. David Lichtenstein
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  4. Nathan Linial
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  5. Avi Wigderson
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Additional information

Communicated by F. Thomson Leighton.

The first author's research was partially supported by NSF Grant No. MCS 820-5167. The third author's research was supported by NSF Grant No. MCS-8204246 and by a Hebrew University Fellowship.

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Aggarwal, A., Klawe, M., Lichtenstein, D. et al. A lower bound on the area of permutation layouts. Algorithmica 6, 241–255 (1991). https://doi.org/10.1007/BF01759044

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  • DOI: https://doi.org/10.1007/BF01759044

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