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A Faster Algorithm for Finding Minimum Tucker Submatrices

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Book cover Programs, Proofs, Processes (CiE 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6158))

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Abstract

A binary matrix has the Consecutive Ones Property (C1P) if its columns can be ordered in such a way that all 1s on each row are consecutive. Algorithmic issues of the C1P are central in computational molecular biology, in particular for physical mapping and ancestral genome reconstruction. In 1972, Tucker gave a characterization of matrices that have the C1P by a set of forbidden submatrices, and a substantial amount of research has been devoted to the problem of efficiently finding such a minimum size forbidden submatrix. This paper presents a new O(Δ3 m 2 (mΔ + n 3)) time algorithm for this particular task for a m ×n binary matrix with at most Δ 1-entries per row, thereby improving the O(Δ3 m 2(mn + n 3)) time algorithm of Dom et al. [17].

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Author information

Authors and Affiliations

  1. LIGM - UMR CNRS 8049, Université Paris-Est, France

    Guillaume Blin & Stéphane Vialette

  2. Dipartimento di Matematica ed Informatica (DIMI), Universit degli Studi di Udine, Italy

    Romeo Rizzi

Authors
  1. Guillaume Blin
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  2. Romeo Rizzi
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  3. Stéphane Vialette
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Editor information

Editors and Affiliations

  1. Departamento de Matemática, Universidade de Lisboa, Campo Grande, Edifício C6, 1749-016, Lisboa, Portugal

    Fernando Ferreira

  2. Institute for Logic, Language and Computation (ILLC), Universiteit van Amsterdam, P.O. Box 94242, 1090, Amsterdam, GE, The Netherlands

    Benedikt Löwe

  3. Departamento de Informática e Ingeniería de Sistemas, Universidad de Zaragoza, María de Luna 1, 50018, Zaragoza, Spain

    Elvira Mayordomo

  4. Universidade dos Açores, Campus de Ponta Delgada, Apartado 1422, 9501-801, Ponta Delgada, Açores, Portugal

    Luís Mendes Gomes

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Blin, G., Rizzi, R., Vialette, S. (2010). A Faster Algorithm for Finding Minimum Tucker Submatrices. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_8

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  • DOI: https://doi.org/10.1007/978-3-642-13962-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13961-1

  • Online ISBN: 978-3-642-13962-8

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