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Exploiting Restricted Linear Structure to Cope with the Hardness of Clique-Width

  • Conference paper
Theory and Applications of Models of Computation (TAMC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6108))

Abstract

Clique-width is an important graph parameter whose computation is NP-hard. In fact we do not know of any algorithm other than brute force for the exact computation of clique-width on any graph class of unbounded clique-width, other than square grids. Results so far indicate that proper interval graphs constitute the first interesting graph class on which we might have hope to compute clique-width, or at least its variant linear clique-width, in polynomial time. In TAMC 2009, a polynomial-time algorithm for computing linear clique-width on a subclass of proper interval graphs was given. In this paper, we present a polynomial-time algorithm for a larger subclass of proper interval graphs that approximates the clique-width within an additive factor 3. Previously known upper bounds on clique-width result in arbitrarily large difference from the actual clique-width when applied on this class. Our results contribute toward the goal of eventually obtaining a polynomial-time exact algorithm for clique-width on proper interval graphs.

This work was supported by Deutsche Forschungsgemeinschaft, grant RO 927/7, and by the Reseach Council of Norway.

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References

  1. Brandstädt, A., Dragan, F., Le, H.-O., Mosca, R.: New Graph Classes of Bounded Clique-Width. Theory of Computing Systems 38, 623–645 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Corneil, D.G., Habib, M., Lanlignel, J.-M., Reed, B.A., Rotics, U.: Polynomial Time Recognition of Clique-Width ≤ 3 Graphs (Extended Abstract). In: Gonnet, G.H., Viola, A. (eds.) LATIN 2000. LNCS, vol. 1776, pp. 126–134. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  3. Corneil, D.G., Rotics, U.: On the Relationship between Clique-width and Treewidth. SIAM Journal on Computing 34, 825–847 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Courcelle, B., Engelfriet, J., Rozenberg, G.: Handle-rewriting hypergraph grammars. Journal of Computer and System Sciences 46, 218–270 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  5. Courcelle, B., Makowsky, J.A., Rotics, U.: Linear time solvable optimization problems on graphs of bounded clique-width. Theory of Computing Systems 33, 125–150 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Courcelle, B., Olariu, S.: Upper bounds to the clique width of graphs. Discrete Applied Mathematics 101, 77–114 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  7. Espelage, W., Gurski, F., Wanke, E.: Deciding clique-width for graphs of bounded tree-width. Journal of Graph Algorithms and Applications 7, 141–180 (2003)

    MATH  MathSciNet  Google Scholar 

  8. Fellows, M.R., Rosamond, F.A., Rotics, U., Szeider, S.: Clique-Width is NP-Complete. SIAM Journal on Discrete Mathematics 23, 909–939 (2009)

    Article  MathSciNet  Google Scholar 

  9. Golumbic, M.C., Rotics, U.: On the Clique-Width of Some Perfect Graph Classes. International Journal of Foundations of Computer Science 11, 423–443 (2000)

    Article  MathSciNet  Google Scholar 

  10. Heggernes, P., Meister, D., Papadopoulos, C.: A new representation of proper interval graphs with an application to clique-width. Electronic Notes in Discrete Mathematics 32, 27–34 (2009)

    Article  Google Scholar 

  11. Heggernes, P., Meister, D., Papadopoulos, C.: A Complete Characterisation of the Linear Clique-Width of Path Powers. In: Chen, J., Cooper, S.B. (eds.) TAMC 2009. LNCS, vol. 5532, pp. 241–250. Springer, Heidelberg (2009)

    Google Scholar 

  12. Hlinený, P., Oum, S.-I.: Finding branch-decompositions and rank-decompositions. SIAM Journal on Computing 38, 1012–1032 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  13. Hlinený, P., Oum, S.-I., Seese, D., Gottlob, G.: Width parameters beyond tree-width and their applications. The Computer Journal 51, 326–362 (2008)

    Article  Google Scholar 

  14. Lozin, V.: From tree-width to clique-width: excluding a unit interval graph. In: Hong, S.-H., Nagamochi, H., Fukunaga, T. (eds.) ISAAC 2008. LNCS, vol. 5369, pp. 872–883. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  15. Lozin, V., Rautenbach, D.: Chordal bipartite graphs of bounded tree- and clique-width. Discrete Mathematics 283, 151–158 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  16. Lozin, V., Rautenbach, D.: On the Band-, Tree-, and Clique-Width of Graphs with Bounded Vertex Degree. SIAM Journal on Discrete Mathematics 18, 195–206 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  17. Müller, H., Urner, R.: On a disparity between relative cliquewidth and relative NLC-width. Discrete Applied Mathematics (to appear)

    Google Scholar 

  18. Oum, S.-I.: Approximating rank-width and clique-width quickly. ACM Transactions on Algorithms 5 (2008)

    Google Scholar 

  19. Oum, S.-I., Seymour, P.: Approximating clique-width and branch-width. Journal on Combinatorial Theory, Series B 96, 514–528 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  20. Roberts, F.S.: Indifference graphs. In: Harary, F. (ed.) Proof techniques in graph theory, pp. 139–146. Academic Press, New York (1969)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, Norway

    Pinar Heggernes

  2. Theoretical Computer Science, RWTH Aachen University, Germany

    Daniel Meister

  3. Netanya Academic College, Netanya, Israel

    Udi Rotics

Authors
  1. Pinar Heggernes
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  2. Daniel Meister
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  3. Udi Rotics
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Editor information

Editors and Affiliations

  1. Charles University, Malostranske nam 25, 11800, Praha 1, Czech Republic

    Jan Kratochvíl , Jiří Fiala  & Petr Kolman ,  & 

  2. State Key Lab. of Computer Science, Institute of Software,, Chinese Academy of Sciences, 100190, Beijing, P.R. China

    Angsheng Li

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Heggernes, P., Meister, D., Rotics, U. (2010). Exploiting Restricted Linear Structure to Cope with the Hardness of Clique-Width. In: Kratochvíl, J., Li, A., Fiala, J., Kolman, P. (eds) Theory and Applications of Models of Computation. TAMC 2010. Lecture Notes in Computer Science, vol 6108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13562-0_26

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  • DOI: https://doi.org/10.1007/978-3-642-13562-0_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13561-3

  • Online ISBN: 978-3-642-13562-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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