Abstract

Given a planar graph G together with a planar representation P, a region preserving grid embedding of G is a planar embedding of G in the rectilinear grid that has planar representation isomorphic to P. In this paper, an algorithm is presented that computes a region preserving grid embedding with the minimum number of bends in edges. This algorithm makes use of network flow techniques, and runs in time $O(n^2 \log n)$, where n is the number of vertices of the graph. Constrained versions of the problem are also considered, and most results are extended to k-gonal graphs, i.e., graphs whose edges are sequences of segments with slope multiple of ${{180} / k}$ degrees. Applications of the above results can be found in several areas: VLSI circuit layout, architectural design, communication by light or microwave, transportation problems, and automatic layout of graphlike diagrams.

MSC codes

  1. 68U05
  2. 68R10
  3. 68Q35
  4. 94C15
  5. 90B10

Keywords

  1. planar embedding
  2. grid
  3. VLSI layout
  4. bends
  5. network flow

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References

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Information & Authors

Information

Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 421 - 444
ISSN (online): 1095-7111

History

Submitted: 3 October 1984
Accepted: 30 June 1986
Published online: 13 July 2006

MSC codes

  1. 68U05
  2. 68R10
  3. 68Q35
  4. 94C15
  5. 90B10

Keywords

  1. planar embedding
  2. grid
  3. VLSI layout
  4. bends
  5. network flow

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