O(n/sup 2/) algorithms for graph planarization

• Published in: IEEE transactions on computer-aided design of integrated circuits and systems Vol. 8; no. 3; pp. 257 - 267
• Main Authors: Jayakumar, R., Thulasiraman, K., Swamy, M.N.S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.1989; Institute of Electrical and Electronics Engineers
• Subjects: Combinatorics; Combinatorics. Ordered structures; Computer science; Councils; Design automation; Electronic circuits; Exact sciences and technology; Graph theory; Mathematics; NP-complete problem; Planarization; Printed circuits; Sciences and techniques of general use; Testing; Wire; Biconnected graph; Graph theory; Planar graph; Algorithm complexity
• ISSN: 0278-0070
• DOI: 10.1109/43.21845

The authors present two O(n/sup 2/) planarization algorithms, PLANARIZE and MAXIMAL-PLANARIZE. These algorithms are based on A. Lempel, S. Even, and I. Cederbaum's (1967) planarity testing algorithm and its implementation using PQ-trees. Algorithm PLANARIZE is for the construction of a spanning planar subgraph of an n-vertex nonplanar graph. The algorithm proceeds by embedding one vertex at a time and, at each step, adds the maximum number of edges possible without creating nonplanarity of the resultant graph. Given a biconnected spanning planar subgraph G/sub p/ of a nonplanar graph G, the MAXIMAL-PLANARIZE algorithm constructs a maximal planar subgraph of G which contains G/sub p/. This latter algorithm can also be used to planarize maximally a biconnected planar graph.< >