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New Upper Bound Heuristics for Treewidth

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Experimental and Efficient Algorithms (WEA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 3503))

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Abstract

In this paper, we introduce and evaluate some heuristics to find an upper bound on the treewidth of a given graph. Each of the heuristics selects the vertices of the graph one by one, building an elimination list. The heuristics differ in the criteria used for selecting vertices. These criteria depend on the fill-in of a vertex and the related new notion of the fill-in-excluding-one-neighbor. In several cases, the new heuristics improve the bounds obtained by existing heuristics.

This work has been supported by the Netherlands Organization for Scientific Research NWO (project TACO: ’Treewidth And Combinatorial Optimization’).

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References

  1. Amir, E.: Efficient approximation for triangulation of minimum treewidth. In: Proceedings of the 17th Conference on Uncertainty in Artificial Intelligence, UAI 2001, Seattle, Washington, USA, pp. 7–15 (2001)

    Google Scholar 

  2. Arnborg, S., Corneil, D.G., Proskurowski, A.: Complexity of finding embeddings in a k-tree. SIAM Journal on Algebraic and Discrete Methods 8, 277–284 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bodlaender, H.L.: Discovering treewidth. In: Vojtáš, P., Bieliková, M., Charron-Bost, B., Sýkora, O. (eds.) SOFSEM 2005. LNCS, vol. 3381, pp. 1–16. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Bodlaender, H.L., Koster, A.M.C.A., van den Eijkhof, F., van der Graag, L.C.: Preprocessing for triangulation of probabilistic networks. In: Breese, J., Koller, D. (eds.) Proceedings of the 17th Conference on Uncertainty in Artificial Intelligence, pp. 32–39. Morgan Kaufmann Publishers, San Francisco (2001)

    Google Scholar 

  5. Bodlaender, H.L.: A partial k-arboretum of graphs with bounded treewidth. Theoretical Computer Science 209, 1–45 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bodlaender, H.L.: A tourist guide through treewidth. Acta Cybernetica 11(1-2), 1–21 (1993)

    MATH  MathSciNet  Google Scholar 

  7. Clautiaux, F., Carlier, J., Moukrim, A., Negre, S.: New lower and upper bounds for graph treewidth. In: Jansen, K., Margraf, M., Mastrolli, M., Rolim, J.D.P. (eds.) WEA 2003. LNCS, vol. 2647, pp. 70–80. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  8. Columbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Academic Press, Inc., London (1980)

    Google Scholar 

  9. Cook, W., Seymour, P.D.: Tour Merging via branch-decomposition. Informs J. on Computing 15, 233–248 (2003)

    Article  MathSciNet  Google Scholar 

  10. Kornai, A., Tuza, Z.: Narrowness, pathwidth, and their application in natural language processing. Discrete Application Mathematics 36, 87–92 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  11. Koster, A.M.C.A., Bodlaender, H.L., van Hoesel, S.: Treewidth: Computational experiments. In: Broersma, H., Faigle, U., Hurink, J., Pickl, S. (eds.) Electronic Notes in Discrete Mathematics, vol. 8. Elsevier Science Publishers, Amsterdam (2001)

    Google Scholar 

  12. Koster, A.M.C.A., van Hoesel, C.P.M., Kolen, A.W.J.: Solving frequency assignment problems via tree-decomposition. Technical report RM 99/011, Maastricht University (1999), Available at http://www.zib.de/koster/

  13. Koster, A.M.C.A., van Hoesel, C.P.M., Kolen, A.W.J.: Lower bounds for minimum interference frequency assignment problems. Ricerca Operativa 30(94-95), 101–116 (2000)

    Google Scholar 

  14. Koster, A.M.C.A.: Frequency Assignment? Models and Algorithms. PhD thesis, Maastricht University, Maastricht, the Netherlands (1999)

    Google Scholar 

  15. Lauritzen, S.J., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their application to expert systems. The Journal of the Royal Statistical Society, Series B (Methodological) 50, 157–224 (1988)

    MATH  MathSciNet  Google Scholar 

  16. Rose, D.J., Tarjan, R.E., Lueker, G.S.: Algorithmic aspects of vertex elimination on graphs. SIAM Journal on Computing 5, 266–283 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  17. Shoikhet, K., Geiger, D.: A practical algorithm for finding optimal triangulations. In: Proceeding National conference on Artificial Intelligence (AAAI 1997), pp. 185–190. Morgan Kaufmann, San Francisco (1997)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB, Utrecht, The Netherlands

    Emgad H. Bachoore & Hans L. Bodlaender

Authors
  1. Emgad H. Bachoore
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  2. Hans L. Bodlaender
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Editor information

Editors and Affiliations

  1. CTI and Univ. of Patras, Greece

    Sotiris E. Nikoletseas

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© 2005 Springer-Verlag Berlin Heidelberg

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Bachoore, E.H., Bodlaender, H.L. (2005). New Upper Bound Heuristics for Treewidth. In: Nikoletseas, S.E. (eds) Experimental and Efficient Algorithms. WEA 2005. Lecture Notes in Computer Science, vol 3503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427186_20

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  • DOI: https://doi.org/10.1007/11427186_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25920-6

  • Online ISBN: 978-3-540-32078-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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