Two Algorithms for Finding Rectangular Duals of Planar Graphs

نویسندگان

  • Goos Kant
  • Xin He
چکیده

1 I n t r o d u c t i o n The problem of drawing a graph on the plane has received increasing attention due to a large number of applications [3]. Examples include VLSI layout, algorithm animation, visual languages and CASE tools. Vertices are usually represented by points and edges by curves. In the design of floor planning of electronic chips and in architectural design, it is also common to represent a graph G by a rectangular dual, defined as follows. A rectangular subdivision system of a rectangle R is a partition of R into a set F = {R1, R2 , . . . , R,~}. of non-overlapping rectangles such that no four rectangles in F meet at the samepoint. A rectangular dual of a planar graph G = (V, E) is a rectangular subdivision system Y' and a one-to-one correspondence f : V --+ F such that two vertices u and v are adjacent in G if and only if th6ir corresponding rectangles f(u) and f(v) share a common boundary. In the application of this representation, the vertices of G represent circuit modules and the edges represent module adjacencies. A-rectangular dual provides a placement of the circuit modules that preserves the required ad]acencies. Figure 1 shows an example of a planar graph and its rectangular dual. This problem was studied in [1, 2, 8]. Bhasker and Sahni gave a linear time algorithm to construct rectangular duals [2]. The algorithm is fairly complicated and requires many intriguing procedures. The coordinates of the rectangular dual constructed by it are real numbers and bear no meaningful relationship with the * The work Of the first author was supported by the ESPRIT Basic Research Actions program of the EC under contract No. 7141 (project ALCOM II). The work of the second author was supported by National Science Foundation, grant number CCR-9011214.

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تاریخ انتشار 1993