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Linear Layouts in Submodular Systems

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Algorithms and Computation (ISAAC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7676))

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Abstract

Linear layout of graphs/digraphs is one of the classical and important optimization problems that have many practical applications. Recently Tamaki proposed an O(mn k + 1)-time and O(n k)-space algorithm for testing whether the pathwidth (or vertex separation) of a given digraph with n vertices and m edges is at most k. In this paper, we show that linear layout of digraphs with an objective function such as cutwidth, minimum linear arrangement, vertex separation (or pathwidth) and sum cut can be formulated as a linear layout problem on a submodular system (V,f) and then propose a simple framework of search tree algorithms for finding a linear layout (a sequence of V) with a bounded width that minimizes a given cost function. According to our framework, we obtain an O( k m n 2k)-time and O(n + m)-space algorithm for testing whether the pathwidth of a given digraph is at most k.

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Author information

Authors and Affiliations

  1. Graduate School of Informatics, Kyoto University, Japan

    Hiroshi Nagamochi

Authors
  1. Hiroshi Nagamochi
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taiwan University, 1 Roosevelt Road, Section 4, 106, Taipei, Taiwan

    Kun-Mao Chao

  2. Institute of Information Science, Academia Sinica, 128 Academia Road, Section 2, 115, Taipei, Taiwan

    Tsan-sheng Hsu

  3. Department of Computer Science and Engineering, National Chung Hsing University, 250 Kuo Kuang Road, 402, Taichung, Taiwan

    Der-Tsai Lee

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© 2012 Springer-Verlag Berlin Heidelberg

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Nagamochi, H. (2012). Linear Layouts in Submodular Systems. In: Chao, KM., Hsu, Ts., Lee, DT. (eds) Algorithms and Computation. ISAAC 2012. Lecture Notes in Computer Science, vol 7676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35261-4_50

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  • DOI: https://doi.org/10.1007/978-3-642-35261-4_50

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35260-7

  • Online ISBN: 978-3-642-35261-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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