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Efficient Analy sis of Graphs with Small Minimal Separators

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Graph-Theoretic Concepts in Computer Science (WG 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1665))

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Abstract

We consider the class C* of graphs whose minimal separators have a fixed bounded size. We give an O(nm)-time algorithm computing an optimal tree-decomposition of every graph in C* with n vertices and m edges. Furthermore we make evident that many NP-complete problems are solvable in polynomial time when restricted to this class. Both claims hold although C* contains graphs of arbitrarily large tree-width.

The work of the author was supported by the German Research Association (DFG) grant BR 835/7-1

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References

  1. S. Arnborg, D. Corneil, and A. Proskurowski. Complexity of finding embeddings in a k-tree. SIAM J. Alg. Disc. Meth., 8:277–284, 1987. 155, 156, 158

    Article  MATH  MathSciNet  Google Scholar 

  2. S. Arnborg, J. Lagergren, and D. Seese. Easy problems for tree-decomposable graphs. J. Algorithms, 12:308–340, 1991. 155

    Article  MATH  MathSciNet  Google Scholar 

  3. S. Arnborg and A. Proskurowski. Linear time algorithms for NP-hard problems restricted to partial k-trees. Disc. Appl. Math., 23:11–24, 1989. 155

    Article  MATH  MathSciNet  Google Scholar 

  4. H. Bodlaender. Dynamic programming algorithms on graphs with bounded treewidth. In Proceedings of the International Colloquium on Automata, Languages and Programming, volume 317 of Lect. Notes in Comput. Sci., pages 105–119. Springer-Verlag, New York/Berlin, 1988. 159

    Google Scholar 

  5. H. Bodlaender. A linear time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput., 25(6):1305–1317, 1996. 155, 158, 162, 163

    Article  MATH  MathSciNet  Google Scholar 

  6. H. Bodlaender, T. Kloks, and D. Kratsch. Treewidth and pathwidth of permutation graphs. SIAM J. Disc. Math., 8:606–616, 1995. 155, 159

    Article  MATH  MathSciNet  Google Scholar 

  7. H. Bodlaender and R. Möhring. The pathwidth and treewidth of cographs. SIAM J. Disc. Math., 6:181–188, 1993. 155, 159

    Article  MATH  Google Scholar 

  8. R. Borie, R. Parker, and C. Tovey. Automatic generation of liner-time algorithms from predicate calculus describtions of problems on recursively constructed graph families. Algorithmica, 7:555–581, 1992. 155

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Brandstädt. Graphen und Algorithmen. B. G. Teubner, Stuttgard, 1994. 158

    Google Scholar 

  10. F. Gavril. Algorithms on clique separable graphs. Disc. Math., 19:159–165, 1977. 159

    Article  MATH  MathSciNet  Google Scholar 

  11. M. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, 1980. 156, 158

    MATH  Google Scholar 

  12. A. Itai, C. Papadimitriou, and J. Szwarcfiter. Hamilton paths in grid graphs. SIAM J. Comput., 11(4):676–686, 1982. 164

    Article  MATH  MathSciNet  Google Scholar 

  13. T. Kloks. Treewidth. Computations and Approximations, volume 842 of Lect. Notes in Comput. Sci. Springer-Verlag, New York/Berlin, 1994. 155, 158

    MATH  Google Scholar 

  14. T. Kloks, H. Bodlaender, H. Müller, and D. Kratsch. Computing treewidth and minimum fill-in: All you need are the minimal separators. In Proceedings of the European Symposium on Algorithms, volume 726 of Lect. Notes in Comput. Sci., pages 260–271. Springer-Verlag, New York/Berlin, 1993. 156

    Google Scholar 

  15. T. Kloks, H. Bodlaender, H. Müller, and D. Kratsch. Erratum to the ESA’93 proceedings. In Proceedings of the European Symposium on Algorithms, volume 855 of Lect. Notes in Comput. Sci., page 508. Springer-Verlag, New York/Berlin, 1994. 156

    Google Scholar 

  16. T. Kloks and D. Kratsch. Treewidth of chordal bipartite graphs. J. Algorithms, 19:266–281, 1995. 155, 159

    Article  MATH  MathSciNet  Google Scholar 

  17. T. Kloks and D. Kratsch. Listing all minimal separators of a graph. SIAM J. Comput., 27(3):605–613, 1998. 156

    Article  MATH  MathSciNet  Google Scholar 

  18. C. Papadimitriou. Computational Complexity. Addison-Wesley Publishing Company, 1994. 164

    Google Scholar 

  19. A. Parra and P. Scheffler. How to use the minimal separators of a graph for its chordal triangulation. In Proceedings of the International Colloquium on Automata, Languages and Programming, volume 944 of Lect. Notes in Comput. Sci., pages 123–134. Springer-Verlag, New York/Berlin, 1995. 156

    Google Scholar 

  20. N. Robertson and P. Seymour. Graph minors X. Obstructions to treedecompositions. J. Comb. Theory Series B, 52:153–190, 1991. 155, 159

    Article  MATH  MathSciNet  Google Scholar 

  21. R. Sundaram, K. Sher Singh, and C. Pandu Rangan. Treewidth of circular-arc graphs. SIAM J. Disc. Math., 7:647–655, 1994. 155, 159

    Article  MATH  MathSciNet  Google Scholar 

  22. R. Tarjan. Decomposition by clique separators. Disc. Math., 55:221–232, 1985. 157, 159, 163

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Passau, 94030, Passau, Germany

    K. Skodinis

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  1. K. Skodinis
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Editor information

Editors and Affiliations

  1. Institute for Theoretical Computer Science ETH Zürich ETH Zentrum, 8092, Zürich, Switzerland

    Peter Widmayer , Gabriele Neyer  & Stephan Eidenbenz ,  & 

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Skodinis, K. (1999). Efficient Analy sis of Graphs with Small Minimal Separators. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds) Graph-Theoretic Concepts in Computer Science. WG 1999. Lecture Notes in Computer Science, vol 1665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46784-X_16

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  • DOI: https://doi.org/10.1007/3-540-46784-X_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66731-5

  • Online ISBN: 978-3-540-46784-7

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