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DOI: 10.4230/LIPIcs.FSTTCS.2023.8

Parameterized Complexity of Biclique Contraction and Balanced Biclique Contraction

Authors: R. Krithika, V. K. Kutty Malu, Roohani Sharma, and Prafullkumar Tale

Published in: LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

Abstract

A bipartite graph is called a biclique if it is a complete bipartite graph and a biclique is called a balanced biclique if it has equal number of vertices in both parts of its bipartition. In this work, we initiate the complexity study of Biclique Contraction and Balanced Biclique Contraction. In these problems, given as input a graph G and an integer k, the objective is to determine whether one can contract at most k edges in G to obtain a biclique and a balanced biclique, respectively. We first prove that these problems are NP-complete even when the input graph is bipartite. Next, we study the parameterized complexity of these problems and show that they admit single exponential-time FPT algorithms when parameterized by the number k of edge contractions. Then, we show that Balanced Biclique Contraction admits a quadratic vertex kernel while Biclique Contraction does not admit any polynomial compression (or kernel) unless NP ⊆ coNP/poly.

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R. Krithika, V. K. Kutty Malu, Roohani Sharma, and Prafullkumar Tale. Parameterized Complexity of Biclique Contraction and Balanced Biclique Contraction. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{krithika_et_al:LIPIcs.FSTTCS.2023.8,
  author =	{Krithika, R. and Malu, V. K. Kutty and Sharma, Roohani and Tale, Prafullkumar},
  title =	{{Parameterized Complexity of Biclique Contraction and Balanced Biclique Contraction}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-304-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{284},
  editor =	{Bouyer, Patricia and Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.8},
  URN =		{urn:nbn:de:0030-drops-193811},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.8},
  annote =	{Keywords: contraction, bicliques, balanced bicliques, parameterized complexity}
}

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Documents authored by Malu, V. K. Kutty

Parameterized Complexity of Biclique Contraction and Balanced Biclique Contraction

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