FPT Algorithms for Path-Transversals and Cycle-Transversals Problems in Graphs

  • Sylvain Guillemot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5018)


In this article, we consider problems on graphs of the following form: given a graph, remove p edges/vertices to achieve some property. The first kind of problems are separation problems on undirected graphs, where we aim at separating distinguished vertices in an graph. The second kind of problems are feedback set problems on group-labelled graphs, where we aim at breaking nonnull cycles in a group-labelled graph. We obtain new FPT algorithms for these different problems. A building stone for our algorithms is a general O *(4 p ) algorithm for a class of problems aiming at breaking a set of paths in a graph, provided that the set of paths has a special property called homogeneity.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chen, J., Liu, Y., Lu, S.: An Improved Parameterized Algorithm for the Minimum Node Multiway Cut Problem. In: Dehne, F., Sack, J.-R., Zeh, N. (eds.) WADS 2007. LNCS, vol. 4619, pp. 495–506. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Chudnovsky, M., Geelen, J., Gerards, B., Goddyn, L.A., Lohman, M., Seymour, P.D.: Packing Non-Zero A-Paths In Group-Labelled Graphs. Combinatorica 5(26), 521–532 (2006)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)Google Scholar
  4. 4.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)Google Scholar
  5. 5.
    Garg, N., Vazirani, V., Yannakakis, M.: Multiway Cuts in Directed and Node Weighted Graphs. In: Shamir, E., Abiteboul, S. (eds.) ICALP 1994. LNCS, vol. 820, pp. 487–498. Springer, Heidelberg (1994)Google Scholar
  6. 6.
    Gupta, A., Talwar, K.: Approximating unique games. In: Proc. SODA 2006, pp. 99–106 (2006)Google Scholar
  7. 7.
    Khot, S.: On the power of unique 2-prover 1-round games. In: Proc. STOC 2002, pp. 767–775 (2002)Google Scholar
  8. 8.
    Marx, D.: Parameterized graph separation problems. Theoretical Computer Science (351), 394–406 (2006)Google Scholar
  9. 9.
    Reed, B., Smith, K., Vetta, A.: Finding odd cycle transversals. Operations Research Letters 32(4), 299–301 (2004)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Sylvain Guillemot
    • 1
  1. 1.LIFL/CNRS/INRIABât. M3 Cité ScientifiqueVilleneuve d’Ascq cedexFrance

Personalised recommendations