Maximum Cardinality Search for Computing Minimal Triangulations of Graphs

Abstract. We present a new algorithm, called MCS-M, for computing minimal triangulations of graphs. LexBFS, 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. Key Words. Chordal graphs, Minimal triangulations, Minimal elimination ordering, Minimal fill.

• Type: Journal
• Year: 2004
• Where: ALGORITHMICA
• Authors: Anne Berry, Jean R. S. Blair, Pinar Heggernes, Barry W. Peyton
• Keywords: Algorithm, ALGORITHMICA 2004, Chordal Graphs, Minimal Triangulations