New Results on the Complexity of Oriented Colouring on Restricted Digraph Classes
Oriented colouring is a quite intuitive generalization of undirected colouring, yet the problem remains NP-hard even on digraph classes with bounded usual directed width measures. In light of this fact, one might ask whether new width measures are required for efficient dealing with this problem or whether further restriction of traditional directed width measures such as DAG-width would suffice. The K-width and DAG-depth measures (introduced by [Ganian et al, IWPEC’09]) are ideal candidates for tackling this question: They are both closely tied to the cops-and-robber games which inspire and characterize the most renowned directed width measures, while at the same time being much more restrictive.
In this paper, we look at the oriented colouring problem on digraphs of bounded K-width and of bounded DAG-depth. We provide new polynomial algorithms for solving the problem on “small” instances as well as new strong hardness results showing that the input restrictions required by our algorithms are in fact “tight”.
KeywordsDirected graph complexity oriented colouring DAG-depth
Unable to display preview. Download preview PDF.
- 5.Ganian, R., Hliněný, P.: Better Polynomial Algorithms on Graphs of Bounded Rank-Width. In: IWOCA 2009, Extended Abstract. LNCS. Springer, Heidelberg (to appear, 2009)Google Scholar
- 6.Ganian, R., Hliněný, P., Kneis, J., Langer, A., Obdržálek, J., Rossmanith, P.: On Digraph Width Measures in Parameterized Algorithmics. In: Chen, J., Fomin, F.V. (eds.) IWPEC 2009. LNCS, vol. 5917, pp. 185–197. Springer, Heidelberg (2009)Google Scholar
- 9.Kanté, M.: The Rank-Width of Directed Graphs. arXiv:0709.1433v3 (2008)Google Scholar
- 10.Nešetřil, J., Ossona de Mendez, P.: Tree-Depth, Subgraph Coloring and Homomorphism Bounds. European J. Combin. 27(6), 1024–1041 (2006)Google Scholar
- 12.Obdržálek, J.: DAG-Width: Connectivity Measure for Directed Graphs. In: SODA 2006, pp. 814–821. ACM-SIAM (2006)Google Scholar