In the Odd Cycle Transversal (OCT) problem we are given a graph G on n vertices and an integer k, the objective is to determine whether there exists a vertex set O in G of size at most k such that G - O is bipartite. Reed, Smith and Vetta [Oper. Res. Lett., 2004] gave an algorithm for OCT with running time 3^kn^{O(1)}. Assuming the exponential time hypothesis of Impagliazzo, Paturi and Zane, the running time can not be improved to 2^{o(k)}n^{O(1)}. We show that OCT admits a randomized algorithm running in O(n^{O(1)} + 2^{O(sqrt{k} log k)}n) time when the input graph is planar. As a byproduct we also obtain a linear time algorithm for OCT on planar graphs with running time O(n^O(1) + 2O( sqrt(k) log k) n) time. This improves over an algorithm of Fiorini et al. [Disc. Appl. Math., 2008].
@InProceedings{lokshtanov_et_al:LIPIcs.FSTTCS.2012.424, author = {Lokshtanov, Daniel and Saurabh, Saket and Wahlstr\"{o}m, Magnus}, title = {{Subexponential Parameterized Odd Cycle Transversal on Planar Graphs}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)}, pages = {424--434}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-47-7}, ISSN = {1868-8969}, year = {2012}, volume = {18}, editor = {D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.424}, URN = {urn:nbn:de:0030-drops-38783}, doi = {10.4230/LIPIcs.FSTTCS.2012.424}, annote = {Keywords: Graph Theory, Parameterized Algorithms, Odd Cycle Transversal} }
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