Plane representations of graphs and visibility between parallel segments
Abstract
Several layout compaction strategies for VLSI are based on the concept of visibility between parallel segments, where we say that two parallel segments of a given set are visible if they can be joined by a segment orthogonal to them, which does not intersect any other segment. This paper studies visibility representations of graphs, which are constructed by mapping vertices to horizontal segments, and edges to vertical segments drawn between visible vertexsegments. Clearly, every graph that admits such a representation must be a planar. The authors consider three types of visibility representations, and give complete characterizations of the classes of graphs that admit them. Furthermore, they present linear time algorithms for testing the existence of and constructing visibility representations of planar graphs.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 April 1985
 Bibcode:
 1985STIN...8621770T
 Keywords:

 Alignment;
 Graphs (Charts);
 Segments;
 Very Large Scale Integration;
 Visibility;
 Algorithms;
 Integrated Circuits;
 Orthogonal Functions;
 Time;
 Electronics and Electrical Engineering