Fixed Parameter Algorithms for Counting and Deciding Bounded Restrictive List H-Colorings
We study the fixed parameter tractability of the parameterized counting and decision version of the restrictive H-coloring problem. These problems are defined by fixing the number of preimages of a subset C of the vertices in H through a partial weight assignment (H,C,K). We consider two families of partial weight assignment the simple and the plain. For simple partial weight assignments we show an FPT algorithm for counting list (H,C,K)-colorings and faster algorithms for its decision version. For the more general class of plain partial weight assignment we give an FPT algorithm for the (H,C,K)-coloring decision problem. We introduce the concept of compactor and an algorithmic technique, compactor enumeration, that allow us to design the FPT algorithms for the counting version (and probably export the technique to other problems).
Unable to display preview. Download preview PDF.
- 1.Díaz, J.: H-colorings of graphs. Bulletin of the European Association for Theoretical Computer Science (75), 82–92 (2001)Google Scholar
- 3.Díaz, J., Serna, M., Thilikos, D.: The restrictive H-coloring problem. Discrete Applied Mathematics (to appear)Google Scholar
- 4.Díaz, J., Serna, M., Thilikos, D.M.: Recent results on parameterized H-colorings Graphs. In: Morphisms and Statistical Physics. DIMACS series in Discrete Mathematics and Theoretical Computer Science, vol. 63, pp. 65–85 (2004)Google Scholar
- 5.Díaz, J., Serna, M., Thilikos, D.M.: Complexity issues on Bounded Restrictive H-colorings (2004) (submitted)Google Scholar
- 6.Downey, R.G., Fellows, M.R.: Parameterized complexity. Springer, New York (1999)Google Scholar
- 13.Hell, P., Nešetřil, J.: Counting list homomorphisms and graphs with bounded degrees. In: Graphs, Morphisms and Statistical Physics. DIMACS series in Discrete Mathematics and Theoretical Computer Science, vol. 63, pp. 105–112 (2004)Google Scholar
- 15.McCartin, C.: Contributions to Parameterized Complexity. PhD thesis, Victoria University of Wellington (2003)Google Scholar