A single-exponential fixed-parameter algorithm for distance-hereditary vertex deletion


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EIBEN Eduard GANIAN Robert KWON O-joung

Year of publication 2018
Type Article in Periodical
Magazine / Source Journal of Computer and System Sciences
MU Faculty or unit

Faculty of Informatics

Doi http://dx.doi.org/10.1016/j.jcss.2018.05.005
Keywords parameterized complexity; distance hereditary graphs
Description Vertex deletion problems ask whether it is possible to delete at most k vertices from a graph so that the resulting graph belongs to a specified graph class. Over the past years, the parameterized complexity of vertex deletion to a plethora of graph classes has been systematically researched. Here we present the first single-exponential fixed-parameter tractable algorithm for vertex deletion to distance-hereditary graphs, a well-studied graph class which is particularly important in the context of vertex deletion due to its connection to the graph parameter rank-width. We complement our result with matching asymptotic lower bounds based on the exponential time hypothesis. As an application of our algorithm, we show that a vertex deletion set to distance-hereditary graphs can be used as a parameter which allows single-exponential fixed-parameter tractable algorithms for classical NP-hard problems.
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