O(n/sup 2/) algorithms for graph planarization
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...
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| Published in | IEEE transactions on computer-aided design of integrated circuits and systems Vol. 8; no. 3; pp. 257 - 267 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.03.1989
Institute of Electrical and Electronics Engineers |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0278-0070 |
| DOI | 10.1109/43.21845 |
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| Abstract | 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.< > |
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| AbstractList | 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.< > The authors present two O( < e1 > n < /e1 > (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 < e1 > PQ < /e1 > -trees. Algorithm PLANARIZE is for the construction of a spanning planar subgraph of an < e1 > n < /e1 > -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 < e1 > G < /e1 > (p) of a nonplanar graph < e1 > G < /e1 > , the MAXIMAL-PLANARIZE algorithm constructs a maximal planar subgraph of < e1 > G < /e1 > which contains < e1 > G < /e1 > (p ). This latter algorithm can also be used to planarize maximally a biconnected planar graph |
| Author | Swamy, M.N.S. Thulasiraman, K. Jayakumar, R. |
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| Cites_doi | 10.1109/31.1746 10.1007/BF02253293 10.1007/3-540-10704-5_9 10.1016/0304-3975(76)90086-4 10.1109/TCT.1966.1082574 10.1145/321850.321852 10.1016/S0022-0000(76)80045-1 |
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| Keywords | Biconnected graph Graph theory Planar graph Algorithm complexity |
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| References | ref13 ref15 ref14 chiba (ref5) 0 ref2 jayakumar (ref12) 1988 ozawa (ref7) 1981; 108 ref8 lempel (ref9) 1966 garey (ref1) 1979 ref6 pasedach (ref3) 1976 even (ref10) 1979 jayakumar (ref11) 1986; cas 33 marek-sadowska (ref4) 0 |
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| Snippet | 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.... The authors present two O( < e1 > n < /e1 > (2)) planarization algorithms, PLANARIZE and MAXIMAL-PLANARIZE. These algorithms are based on A. Lempel, S. Even,... |
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| SubjectTerms | 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 |
| Title | O(n/sup 2/) algorithms for graph planarization |
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