Wire length distribution for placements of computer logic

  • Authors:
  • W. E. Donath

  • Affiliations:
  • IBM Thomas J. Watson Research Center, Yorktown Heights, New Yor

  • Venue:
  • IBM Journal of Research and Development
  • Year:
  • 1981

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Abstract

It is shown from simple theoretical considerations that the distribution fk of wire lengths for a good two-dimensional placement on a square Manhattan grid should be of the form fk = g/kγ (1 ≤ k ≤ L) and fk ≅ 0 (k L), where γ is related to the Rent partitioning exponent p by the equation 2p + γ ≅ 3. Three placements were investigated and the distribution functions for wire length were found to follow the above relationships.