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Applying Modular Decomposition to Parameterized Bicluster Editing

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Parameterized and Exact Computation (IWPEC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4169))

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Abstract

A graph G is said to be a cluster graph if G is a disjoint union of cliques (complete subgraphs), and a bicluster graph if G is a disjoint union of bicliques (complete bipartite subgraphs). In this work, we study the parameterized version of the NP-hard Bicluster Graph Editing problem, which consists of obtaining a bicluster graph by making the minimum number of modifications in the edge set of an input bipartite graph. When at most k modifications are allowed in the edge set of any input graph (Bicluster( k ) Graph Editing problem), this problem is FPT, solvable in O(4k m) time by applying a search tree algorithm. It is shown an algorithm with O(4k + n + m) time, which uses a new strategy based on modular decomposition techniques. Furthermore, the same techniques lead to a new form of obtaining a problem kernel with O(k 2) vertices for the Cluster( k ) Graph Editing problem, in O(n +m) time. This problem consists of obtaining a cluster graph by modifying at most k edges in an input graph. A previous FPT algorithm for this problem was presented by Gramm et al. [11]. In their solution, a problem kernel with O(k 2) vertices and O(k 3) edges is built in O(n 3) time.

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Authors and Affiliations

  1. Instituto de Matemática and Núcleo de Computação Eletrônica, Universidade Federal do Rio de Janeiro, Caixa Postal 2324, 20001-970, Rio de Janeiro, RJ, Brasil

    Fábio Protti

  2. COPPE-Sistemas, Universidade Federal do Rio de Janeiro, Caixa Postal 68511, 21945-970, Rio de Janeiro, RJ, Brasil

    Maise Dantas da Silva

  3. Instituto de Matemática, Núcleo de Computação Eletrônica and COPPE-Sistemas, Universidade Federal do Rio de Janeiro, Caixa Postal 68511, 21945-970, Rio de Janeiro, RJ, Brasil

    Jayme Luiz Szwarcfiter

Authors
  1. Fábio Protti
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  2. Maise Dantas da Silva
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  3. Jayme Luiz Szwarcfiter
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Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, The Netherlands

    Hans L. Bodlaender

  2. University of Tennessee, 37996-3450, Knoxville, Tennessee, U.S.A.

    Michael A. Langston

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© 2006 Springer-Verlag Berlin Heidelberg

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Protti, F., da Silva, M.D., Szwarcfiter, J.L. (2006). Applying Modular Decomposition to Parameterized Bicluster Editing. In: Bodlaender, H.L., Langston, M.A. (eds) Parameterized and Exact Computation. IWPEC 2006. Lecture Notes in Computer Science, vol 4169. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11847250_1

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  • DOI: https://doi.org/10.1007/11847250_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-39098-5

  • Online ISBN: 978-3-540-39101-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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