Abstract
We prove that in an n-vertex graph, an induced planar subgraph of maximum size can be found in time O(1.7347n). This is the first algorithm breaking the trivial 2n n O(1) bound of the brute-force search algorithm for the Maximum Induced Planar Subgraph problem.
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References
Angelsmark, O., Thapper, J.: Partitioning based algorithms for some colouring problems. In: Hnich, B., Carlsson, M., Fages, F., Rossi, F. (eds.) CSCLP 2005. LNCS (LNAI), vol. 3978, pp. 44–58. Springer, Heidelberg (2006)
Bouchitté, V., Mazoit, F., Todinca, I.: Chordal embeddings of planar graphs. Discr. Math. 273(1-3), 85–102 (2003)
Bouchitté, V., Todinca, I.: Treewidth and minimum fill-in: Grouping the minimal separators. SIAM J. Comput. 31(1), 212–232 (2001)
Buneman, P.: A characterization of rigid circuit graphs. Discr. Math. 9, 205–212 (1974)
Eppstein, D.: Subgraph isomorphism in planar graphs and related problems. J. Graph Algorithms Appl. 3(3), 1–27 (1999)
Fomin, F.V., Kratsch, D.: Exact Exponential Algorithms. In: An EATCS Series: Texts in Theoretical Computer Science, Springer, Heidelberg (2010)
Fomin, F.V., Kratsch, D., Todinca, I., Villanger, Y.: Exact algorithms for treewidth and minimum fill-in. SIAM J. Comput. 38(3), 1058–1079 (2008)
Fomin, F.V., Thilikos, D.M.: New upper bounds on the decomposability of planar graphs. Journal of Graph Theory 51(1), 53–81 (2006)
Fomin, F.V., Villanger, Y.: Finding induced subgraphs via minimal triangulations. In: Marion, J.-Y., Schwentick, T. (eds.) STACS. LIPIcs, vol. 5, pp. 383–394. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2010)
Gapers, S., Kratch, D., Liedloff, M.: On independent sets and bicliques in graphs. WG (2008); to appear. Preliminary version in WG
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completness. Freeman, New York (1979)
Gaspers, S.: Exponential Time Algorithms: Structures, Measures, and Bounds. Phd thesis, University of Bergen (2008)
Gavril, F.: The intersection graphs of a path in a tree are exactly the chordal graphs. Journal of Combinatorial Theory 16, 47–56 (1974)
Gupta, S., Raman, V., Saurabh, S.: Fast exponential algorithms for maximum -regular induced subgraph problems. In: Arun-Kumar, S., Garg, N. (eds.) FSTTCS 2006. LNCS, vol. 4337, pp. 139–151. Springer, Heidelberg (2006)
Kreweras, G.: Sur les partition non croisées d’un circle. Discr. Math. 1, 333–350 (1972)
Lewis, J.M., Yannakakis, M.: The node-deletion problem for hereditary properties is np-complete. J. Comput. Syst. Sci. 20(2), 219–230 (1980)
Liebers, A.: Planarizing graphs - a survey and annotated bibliography. Journal of Graph Algorithms and Applications 5 (2001)
Moon, J.W., Moser, L.: On cliques in graphs. Israel Journal of Mathematics 3, 23–28 (1965)
Razgon, I.: Exact computation of maximum induced forest. In: Arge, L., Freivalds, R. (eds.) SWAT 2006. LNCS, vol. 4059, pp. 160–171. Springer, Heidelberg (2006)
Robertson, N., Seymour, P.D.: Graphs minors. II. Algorithmic aspects of tree-width. J. of Algorithms 7, 309–322 (1986)
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Fomin, F.V., Todinca, I., Villanger, Y. (2011). Exact Algorithm for the Maximum Induced Planar Subgraph Problem. In: Demetrescu, C., Halldórsson, M.M. (eds) Algorithms – ESA 2011. ESA 2011. Lecture Notes in Computer Science, vol 6942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23719-5_25
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DOI: https://doi.org/10.1007/978-3-642-23719-5_25
Publisher Name: Springer, Berlin, Heidelberg
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