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Maximum Cardinality Search for Computing Minimal Triangulations of Graphs

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Abstract

We present a new algorithm, called MCS-M, for computing minimal triangulations of graphs. Lex-BFS, a seminal algorithm for recognizing chordal graphs, was the genesis for two other classical algorithms: LEX M and MCS. LEX M extends the fundamental concept used in Lex-BFS, resulting in an algorithm that not only recognizes chordality, but also computes a minimal triangulation of an arbitrary graph. MCS simplifies the fundamental concept used in Lex-BFS, resulting in a simpler algorithm for recognizing chordal graphs. The new algorithm MCS-M combines the extension of LEX M with the simplification of MCS, achieving all the results of LEX M in the same time complexity.

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Authors and Affiliations

  1. LIMOS, UMR CNRS 6158, Université Clermont-Ferrand II, F-63177 Aubiere, France

    Anne Berry

  2. Department of Electrical Engineering and Computer Science, United States Military Academy, West Point, NY 10996, USA

    Jean R. S. Blair

  3. Department of Informatics, University of Bergen, N-5020 Bergen, Norway

    Pinar Heggernes

  4. Division of Natural Sciences and Mathematics, Dalton State College, Dalton, GA 30720, USA

    Barry W. Peyton

Authors
  1. Anne Berry
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  2. Jean R. S. Blair
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  3. Pinar Heggernes
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  4. Barry W. Peyton
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Corresponding authors

Correspondence to Anne Berry, Jean R. S. Blair, Pinar Heggernes or Barry W. Peyton.

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Berry, A., Blair, J., Heggernes, P. et al. Maximum Cardinality Search for Computing Minimal Triangulations of Graphs. Algorithmica 39, 287–298 (2004). https://doi.org/10.1007/s00453-004-1084-3

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  • DOI: https://doi.org/10.1007/s00453-004-1084-3

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