Article Outline
Keywords
Variants and Applications
An Exact Algorithm
Heuristics Based on Planarity Testing
Two-Phase Heuristics
Computational Results
See also
References
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References
Angluin D, Valiant LG (1979) Probabilistic algorithms for Hamiltonian circuits and matchings. J Comput Syst Sci 18:155–190
Booth K, Lueker G (1976) Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. J Comput Syst Sci 13:335–379
Cai J, Han X, Tarjan R (1993) An O(m log n)-time algorithm for the maximal planar subgraph problem. SIAM J Comput 22:1142–1162
Chiba T, Nishioka I, Shirakawa I (1979) An algorithm of maximal planarization of graphs. In: Proc. 1979 IEEE Symp. Circuits and Sys., pp 649–652
Cimikowski RJ (1995) An analysis of heuristics for the maximum planar subgraph problem. In: Proc. 6th ACM-SIAM Symp. Discrete Algorithms, pp 322–331
Di Battista G, Eades P, Tamassia R, Tollis IG (1994) Algorithms for drawing graphs: An annotated bibliography. Comput Geom Th Appl 1:235–282
Di Battista G, Tamassia R (1989) Incremental planarity testing. Proc. 30th IEEE Symp. FOCS, pp 436–441
Eades P, Foulds LR, Giffin JW (1982) An efficient heuristic for identifying a maximum weight planar subgraph. In: Lecture Notes Math, vol 952. Springer, Berlin, pp 239–251
Feo TA, Resende MGC (1995) Greedy randomized adaptive search procedures. J Global Optim 6:109–133
Foulds LR, Robinson RW (1976) A strategy for solving the plant layout problem. Oper Res Quart 27:845–855
Foulds LR, Robinson RW (1978) Graph theoretic heuristics for the plant layout problem. Internat J Production Res 16:27–37
Goldschmidt O, Takvorian A (1994) An efficient graph planarization two-phase heuristic. Networks 24:69–73
Hasan M, Osman IH (1995) Local search algorithms for the maximal planar layout problem. Internat Trans Oper Res 2:89–106
Hopcroft J, Tarjan RE (1974) Efficient planarity testing. J ACM 21:549–568
Jünger M, Leipert S, Mutzel P (1998) A note on computing a maximal planar subgraph using PQ-trees. Techn Report Inst Informatik Univ Köln 98.320
Jünger M, Mutzel P (1996) Maximum planar subgraphs and nice embeddings: Practical layout tools. Algorithmica 16:33–59
Laguna M, Marti R (1999) GRASP and path relinking for 2-layer straight line crossing minimization. INFORMS J Comput 11:44–52
Lempel A, Even S, Cedarbaum I (1966) An algorithm for planarity testing of graphs. Proc. Theory of Graphs Internat. Symp. Gordon and Breach, New York, pp 215–232
Lengauer T (1990) Combinatorial algorithms for integrated circuit layout. Wiley, New York
Leung J (1992) A new graph-theoretic heuristic for facility layout. Managem Sci 38:594–605
Liu PC, Geldmacher RC (1977) On the deletion of nonplanar edges of a graph. In: Proc. 10th SE Conf. Comb., Graph Theory, and Comput., pp 727–738
Resende MGC, Ribeiro CC (1997) A GRASP for graph planarization. Networks 29:173–189
Ribeiro CC, Resende MGC (1999) Algorithm 797: FORTAN subroutines for approximate solution of graph planarization problems using GRASP. ACM Trans Math Softw 25:341–352
Stoer M (1992) Design of survivable networks. Lecture Notes Math, vol 1531. Springer, Berlin
Takefuji Y, Lee KC (1989) A near-optimum parallel planarization algorithm. Science 245:1221–1223
Takefuji Y, Lee K-C, Cho YB (1991) Comments on an O(n2)algorithm for graph planarization. IEEE Trans Computer-Aided Design 10:1582–1583
Tamassia R, DiBattista G (1988) Automatic graph drawing and readability of diagrams. IEEE Trans Syst, Man Cybern 18:61–79
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Resende, M.G., Ribeiro, C.C. (2008). Graph Planarization . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_254
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DOI: https://doi.org/10.1007/978-0-387-74759-0_254
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