Maximum Cardinality Search for Computing Minimal Triangulations of Graphs

Authors:
Anne Berry;Jean R. S. Blair;Pinar Heggernes;Barry W. Peyton
Affiliations:
LIMOS, UMR CNRS 6158, Université Clermont-Ferrand II, F-63177 Aubiere, France;Department of Electrical Engineering and Computer Science, United States Military Academy, West Point, NY 10996, USA;Department of Informatics, University of Bergen, N-5020 Bergen, Norway;Division of Natural Sciences and Mathematics, Dalton State College, Dalton, GA 30720, USA
Venue:
Algorithmica
Year:
2004

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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.