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A linear algorithm for embedding planar graphs using PQ-trees. (English) Zbl 0605.68060
This paper presents a simple linear algorithm for embedding (or drawing) a planar graph in the plane. The algorithm is based on the ”vertex- addition” algorithm of A. Lempel, S. Even, and I. Cederbaum [Theory of graphs, Int. Symp. Rome 1966, 215-232 (1967; Zbl 0197.502)] for the planarity testing, and is a modification of K. S. Booth and G. S. Lueker’s [J. Comput. Syst. Sci. 13, 335-379 (1976; Zbl 0367.68034)] implementation of the testing algorithm using a PQ-tree. Compared with the known embedding algorithm of J. E. Hopcroft and R. E. Tarjan [J. Assoc. Comput. Mach. 21, 549-568 (1974; Zbl 0307.68025)], this algorithm is conceptually simple and easy to understand or implement. Moreover this embedding algorithm can find all the embeddings of a planar graph.

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