{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article8216","name":"Fast Biclustering by Dual Parameterization","abstract":"We study two clustering problems, Starforest Editing, the problem of adding and deleting edges to obtain a disjoint union of stars, and the generalization Bicluster Editing. We show that, in addition to being NP-hard, none of the problems can be solved in subexponential time unless the exponential time hypothesis fails.\r\n \r\nMisra, Panolan, and Saurabh (MFCS 2013) argue that introducing a bound on the number of connected components in the solution should not make the problem easier: In particular, they argue that the subexponential time algorithm for editing to a fixed number of clusters (p-Cluster Editing) by Fomin et al. (J. Comput. Syst. Sci., 80(7) 2014) is an exception rather than the rule. Here, p is a secondary parameter, bounding the number of components in the solution.\r\n\r\nHowever, upon bounding the number of stars or bicliques in the solution, we obtain algorithms which run in time O(2^{3*sqrt(pk)} + n + m) for p-Starforest Editing and O(2^{O(p * sqrt(k) * log(pk))} + n + m) for p-Bicluster Editing. We obtain a similar result for the more general case of t-Partite p-Cluster Editing. This is subexponential in k for a fixed number of clusters, since p is then considered a constant.\r\n \r\nOur results even out the number of multivariate subexponential time algorithms and give reasons to believe that this area warrants further study.","keywords":["graph editing","subexponential algorithms","parameterized complexity"],"author":[{"@type":"Person","name":"Drange, P\u00e5l Gr\u00f8n\u00e5s","givenName":"P\u00e5l Gr\u00f8n\u00e5s","familyName":"Drange"},{"@type":"Person","name":"Reidl, Felix","givenName":"Felix","familyName":"Reidl"},{"@type":"Person","name":"S\u00e1nchez Villaamil, Fernando","givenName":"Fernando","familyName":"S\u00e1nchez Villaamil"},{"@type":"Person","name":"Sikdar, Somnath","givenName":"Somnath","familyName":"Sikdar"}],"position":34,"pageStart":402,"pageEnd":413,"dateCreated":"2015-11-19","datePublished":"2015-11-19","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Drange, P\u00e5l Gr\u00f8n\u00e5s","givenName":"P\u00e5l Gr\u00f8n\u00e5s","familyName":"Drange"},{"@type":"Person","name":"Reidl, Felix","givenName":"Felix","familyName":"Reidl"},{"@type":"Person","name":"S\u00e1nchez Villaamil, Fernando","givenName":"Fernando","familyName":"S\u00e1nchez Villaamil"},{"@type":"Person","name":"Sikdar, Somnath","givenName":"Somnath","familyName":"Sikdar"}],"copyrightYear":"2015","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.IPEC.2015.402","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6246","volumeNumber":43,"name":"10th International Symposium on Parameterized and Exact Computation (IPEC 2015)","dateCreated":"2015-11-19","datePublished":"2015-11-19","editor":[{"@type":"Person","name":"Husfeldt, Thore","givenName":"Thore","familyName":"Husfeldt"},{"@type":"Person","name":"Kanj, Iyad","givenName":"Iyad","familyName":"Kanj"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article8216","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6246"}}}