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International Symposium on Algorithms and Computation

ISAAC 2003: Algorithms and Computation pp 47–57Cite as

A Vertex Incremental Approach for Dynamically Maintaining Chordal Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2906))

Abstract

For a chordal graph G, we study the problem of whether a new vertex u and a given set of edges between u and vertices of G can be added to G so that the resulting graph remains chordal. We show how to resolve this efficiently, and at the same time, if the answer is no, define a maximal subset of the proposed edges that can be added, or conversely a minimal set of extra edges that should be added in addition to the given set. Based on these results, we present a new algorithm which computes both a minimal triangulation and a maximal chordal subgraph of an arbitrary input graph in O(nm) time. This time complexity matches the best known time bound for minimal triangulation, using a totally new vertex incremental approach. In opposition to previous algorithms, our process adds each new vertex without reconsidering any choice made at previous steps, and without requiring any knowledge of the vertices that might be added at further steps.

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Author information

Authors and Affiliations

  1. ISIMA, Univ Clermont-Ferrand II, 63177, Aubiere, France

    Anne Berry

  2. Informatics, Univ of Bergen, 5020, Bergen, Norway

    Pinar Heggernes & Yngve Villanger

Authors
  1. Anne Berry
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  2. Pinar Heggernes
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  3. Yngve Villanger
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Editor information

Editors and Affiliations

  1. School of Science and Technology, Kwansei Gakuin University, Sanda, Japan

    Toshihide Ibaraki

  2. Department of Architecture and Architectural Engineering, Kyoto University, 615-8540, Nishikyo-ku, Kyoto, Japan

    Naoki Katoh

  3. Department of Computer Science and Communication Engineering, Kyushu University, 812-8581, Fukuoka, Japan

    Hirotaka Ono

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© 2003 Springer-Verlag Berlin Heidelberg

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Berry, A., Heggernes, P., Villanger, Y. (2003). A Vertex Incremental Approach for Dynamically Maintaining Chordal Graphs. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_7

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  • DOI: https://doi.org/10.1007/978-3-540-24587-2_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20695-8

  • Online ISBN: 978-3-540-24587-2

  • eBook Packages: Springer Book Archive

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