[Back]

E. Eiben, R. Ganian, O. Kwon:
"A single-exponential fixed-parameter algorithm for distance-hereditary vertex deletion";
Journal of Computer and System Sciences, 96 (2018), 121 - 146.

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.

http://dx.doi.org/10.1016/j.jcss.2018.05.005

https://publik.tuwien.ac.at/files/publik_276175.pdf