Abstract
We present a fixed parameter tractable algorithm for the Independent Set problem in 2-dir graphs and also its generalization to d -dir graphs. A graph belongs to the class of d -dir graphs if it is an intersection graph of segments in at most d directions in the plane. Moreover our algorithms are robust in the sense that they do not need the actual representation of the input graph and they answer correctly even if they are given a graph from outside the promised class.
Supported by project 1M0021620808 of the Ministry of Education of the Czech Republic.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bang-Jensen, J., Reed, B., Schacht, M., Šámal, R., Toft, B., Wagner, U.: On six problems posed by Jarik Nešetřil. In: Klazar, M., Kratochvil, J., Loebl, M., Matousek, J., Valtr, P., Thomas, R. (eds.) Topics in Discrete Mathematics (Dedicated to Jarik Nešetřil on the occasion of his 60th birthday). Springer, Heidelberg (to appear, 2006)
Booth, K.S., Lueker, G.S.: Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. J. Comput. Syst. Sci. 13, 335–379 (1976)
Downey, R.G., Fellows, M.R.: Parametrized Complexity. Springer, Heidelberg (1999)
Garey, M., Johnson, D.: Computers and Intractability. A Guide to the Theory of NP-Completeness. Harry Freeman, New York (1979)
Kratochvíl, J.: A special planar satisfiability problem and a consequence of its NP–completeness. Discrete Appl. Math. 52, 233–252 (1994)
Kratochvíl, J., Matoušek, J.: Intersection graphs of segments. Journal of Combinatorial Theory Series B 62, 289–315 (1994)
Kratochvíl, J., Nešetřil, J.: INDEPENDENT SET and CLIQUE problems in intersection defined classes of graphs. Comment. Math. Univ. Carolin. 31, 85–93 (1990)
Marx, D.: Parameterized Complexity of Independence and Domination on Geometric Graphs. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 154–165. Springer, Heidelberg (2006)
Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)
Roberts, F.S.: Indifference graphs. In: Harary, F. (ed.) Proof Techniques in Graph Theory, pp. 139–146. Academic Press, New York (1969)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kára, J., Kratochvíl, J. (2006). Fixed Parameter Tractability of Independent Set in Segment Intersection Graphs. In: Bodlaender, H.L., Langston, M.A. (eds) Parameterized and Exact Computation. IWPEC 2006. Lecture Notes in Computer Science, vol 4169. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11847250_15
Download citation
DOI: https://doi.org/10.1007/11847250_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-39098-5
Online ISBN: 978-3-540-39101-2
eBook Packages: Computer ScienceComputer Science (R0)