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 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.
@InProceedings{eiben_et_al:LIPIcs.MFCS.2016.34, author = {Eiben, Eduard and Ganian, Robert and Kwon, O-joung}, title = {{A Single-Exponential Fixed-Parameter Algorithm for Distance-Hereditary Vertex Deletion}}, booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)}, pages = {34:1--34:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-016-3}, ISSN = {1868-8969}, year = {2016}, volume = {58}, editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.34}, URN = {urn:nbn:de:0030-drops-64483}, doi = {10.4230/LIPIcs.MFCS.2016.34}, annote = {Keywords: distance-hereditary graphs, fixed-parameter algorithms, rank-width} }
Feedback for Dagstuhl Publishing