Fixed parameter tractability of independent set in segment intersection graphs

Authors:
Jan Kára;Jan Kratochvíl
Affiliations:
Department of Applied Mathematics and Institute for Theoretical Computer Science, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic;Department of Applied Mathematics and Institute for Theoretical Computer Science, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Venue:
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Year:
2006

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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.