0(n2) Algorithms for Graph Planarization

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

Volumn 8, Issue 3, 1989, Pages 257-267

  Jayakumar, R ^a   Thulasiraman, K ^a   Swamy, M N S ^a  

^a Gina Cody School of Engineering and Computer Science   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER PROGRAMMING--ALGORITHMS;

BICONNECTED PLANAR GRAPH; GRAPH PLANARIZATION; NONPLANAR GRAPH; PLANAR SUBGRAPH; PLANARIZATION ALGORITHMS;

MATHEMATICAL TECHNIQUES;

EID: 0024627774     PISSN: 02780070     EISSN: 19374151     Source Type: Journal    
DOI: 10.1109/43.21845     Document Type: Article

References (15)

1. M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness. San Francisco, CA: Freeman, 1979.
2. G.J. Fisher and O. Wing, “Computer recognition and extraction of planar graphs from the incidence matrix,” IEEE Trans. Circuit Theory, vol. CT-13, pp. 154–163, June 1966.
3. K. Pasedach, “Criterion and algorithms for determination of bipartite subgraphs and their application to planarization of graphs,” in Graphen-Sprachen und Algorithmen auf Graphen, Germany: Carl Hanser Verlag, pp. 175–183, 1976.
4. M. Marek-Sadowska, “Planarization algorithm for integrated circuits engineering,” in Proc. 1978 IEEE Int. Symp. on Circuits and Systems, pp. 919–923.
5. T. Chiba, I. Nishioka, and I. Shirakawa, “An algorithm of maximal planarization of graphs,” in Proc. 1979 IEEE Int. Symp. on Circuits and Systems, pp. 649–652.
6. J. Hopcroft and R. Tarjan, “Efficient planarity testing,” /. Ass. Comput. Mach., vol. 21, no. 4, pp. 549–568, Oct. 1974.
7. T. Ozawa and H. Takahashi, “A graph-planarization algorithm and its application to random graphs,” in Graph Theory and Algorithms, Springer-Verlag Lecture Notes in Computer Science, vol. 108, pp. 95–107, 1981.
8. K.S. Booth and G.S. Lueker, “Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms,”. Comp. Syst. Sci., vol. 13, no. 3, pp. 335–379, Dec. 1976.
9. A. Lempel, S. Even, and I. Cederbaum, “An algorithm for planarity testing of graphs,” in Int. Symp. on Theory of Graphs, Rome, Italy, July 1966. P. Rosenstiehl (Ed.), Gordon and Breach, New York, pp. 215–232, 1967.
10. S. Even, Graph Algorithms. Potomac, MD: Computer Sci., Maryland, 1979.
11. R. Jayakumar, K. Thulasiraman, and M.N.S. Swamy, “On maximal planarization of nonplanar graphs,” IEEE Trans. Circuits Syst., vol. CAS-33, no. 8, August 1986, pp. 843–844.
12. R. Jayakumar, “0(n2) algorithms for graph planarization,” Tech. Rep. CSD- 88–01, Dep. of Comp. Sci., Concordia Univ., Montreal, Canada, June 1988.
13. S. Even and R.E. Tarjan, “Computing an.((-numbering,' Theo. Comp. Sci., vol. 2, pp. 339–344, 1976.
14. J. Ebert, “St-ordering the vertices of biconnected graphs,” Computing, vol. 30, pp. 19–33, 1983.
15. R. Jayakumar, K. Thulasiraman, and M.N.S. Swamy, “Planar embedding: linear time algorithms for vertex placement and edge ordering,” IEEE Trans. Circuits Syst., vol. CAS-35, pp. 334–344, Mar. 1988.