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A linear time algorithm to check for the existence of a rectangular dual of a planar triangulated graph. (English) Zbl 0672.05025
Let G be a graph representing a rectangular chip; the vertices of G represent circuit clusters or functional modules that are to be assigned a rectangular space on the chip and an edge (i,j) represents the requirement that modules i and j are adjacent. A rectangular dual of G is an assignment of modules to non-overlapping rectangular areas on the chip such that module adjacencies specified by the edges are satisfied. Necessary and sufficient conditions for the existence of a rectangular dual when G is planar are:
1. Every face (except the exterior) is a triangle,
2. All internal vertices have degree \(\geq 4,\)
3. All cycles that are not faces have length \(\geq 4.\)
The authors develop on O(n) algorithm to determine if a planar graph G satisfies conditions 1 and 3 above. They prove that if conditions 1 and 3 are satisfied, then so is condition 2. Their algorithm restricts attention to biconnected components of G.
Reviewer: L.Caccetta

MSC:
05C10 Planar graphs; geometric and topological aspects of graph theory
68R10 Graph theory (including graph drawing) in computer science
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