Abstract
We introduce a new way to compute common intervals of K permutations based on a very simple and general notion of generators of common intervals. This formalism leads to simple and efficient algorithms to compute the set of all common intervals of K permutations, that can contain a quadratic number of intervals, as well as a linear space basis of this set of common intervals. Finally, we show how our results on permutations can be used for computing the modular decomposition of graphs in linear time.
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Bérard, S., Bergeron, A., Chauve, C.: Conserved structures in evolution scenarios. In: Lagergren, J. (ed.) RECOMB-WS 2004. LNCS (LNBI), vol. 3388, pp. 1–15. Springer, Heidelberg (2005)
Bergeron, A., Chauve, C., de Montgolfier, F., Raffinot, M.: Computing common intervals of K permutations, with applications to modular decomposition of graphs. LIAFA technical report 2005-006, available at: http://www.liafa.jussieu.fr/web9/rapportrech/listrapport_fr.php?anscol=2005
Booth, S., Lueker, G.: Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-trees algorithms. J. Comput. Syst. Sci. 13, 335–379 (1976)
Bui Xuan, B.M., Habib, M., Paul, C.: From Permutations to Graph Algorithms, LIRMM technical report RR-05021 (2005)
Capelle, C., Habib, M.: Graph decompositions and factorizing permutations. In: Fifth Israel Symposium on Theory of Computing and Systems, ISTCS 1997, pp. 132–143. IEEE Computer Society Press, Los Alamitos (1997)
Cournier, A., Habib, M.: A new linear algorithm for modular decomposition. In: Tison, S. (ed.) CAAP 1994. LNCS, vol. 787, pp. 68–84. Springer, Heidelberg (1994)
Dahlhaus, E., Gustedt, J., McConnell, R.M.: Efficient and practical algorithms for sequential modular decomposition. J. Algorithms 41(2), 360–387 (2001)
Figeac, M., Varré, J.-S.: Sorting by reversals with common intervals. In: Jonassen, I., Kim, J. (eds.) WABI 2004. LNCS (LNBI), vol. 3240, pp. 26–37. Springer, Heidelberg (2004)
Habib, M., de Montgolfier, F., Paul, C.: A Simple Linear-Time Modular Decomposition Algorithm for Graphs, Using Order Extension. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 187–198. Springer, Heidelberg (2004)
Heber, S., Stoye, J.: Finding all common intervals of k permutations. In: Amir, A., Landau, G.M. (eds.) CPM 2001. LNCS, vol. 2089, pp. 207–218. Springer, Heidelberg (2001)
Landau, G.M., Parida, L., Weimann, O.: Gene Proximity Analysis Across Whole Genomes via PQ Trees. In: 6th Combinatorial Pattern Matching Conference, CPM (2005)
McConnell, R.M., de Montgolfier, F.: Algebraic Operations on PQ-trees and Modular Decomposition Trees. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, pp. 421–432. Springer, Heidelberg (2005)
McConnell, R.M., Spinrad, J.: Linear-time modular decomposition and efficient transitive orientation of comparability graphs. In: Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 536–545. ACM/SIAM (1994)
McConnell, R.M., Spinrad, J.: Ordered vertex partitioning. Discrete Mathematics & Theoretical Computer Science 4, 45–60 (2000)
Möhring, R.H., Radermacher, F.J.: Substitution decomposition for discrete structures and connections with combinatorial optimization. Annals of Discrete Mathematics 19, 257–356 (1984)
Uno, T., Yagiura, M.: Fast algorithms to enumerate all common intervals of two permutations. Algorithmica 26(2), 290–309 (2000)
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Bergeron, A., Chauve, C., de Montgolfier, F., Raffinot, M. (2005). Computing Common Intervals of K Permutations, with Applications to Modular Decomposition of Graphs. In: Brodal, G.S., Leonardi, S. (eds) Algorithms – ESA 2005. ESA 2005. Lecture Notes in Computer Science, vol 3669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11561071_69
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DOI: https://doi.org/10.1007/11561071_69
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29118-3
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