Computing a Clique Tree with the Algorithm Maximal Label Search
AbstractThe algorithm MLS (Maximal Label Search) is a graph search algorithm that generalizes the algorithms Maximum Cardinality Search (MCS), Lexicographic Breadth-First Search (LexBFS), Lexicographic Depth-First Search (LexDFS) and Maximal Neighborhood Search (MNS). On a chordal graph, MLS computes a PEO (perfect elimination ordering) of the graph. We show how the algorithm MLS can be modified to compute a PMO (perfect moplex ordering), as well as a clique tree and the minimal separators of a chordal graph. We give a necessary and sufficient condition on the labeling structure of MLS for the beginning of a new clique in the clique tree to be detected by a condition on labels. MLS is also used to compute a clique tree of the complement graph, and new cliques in the complement graph can be detected by a condition on labels for any labeling structure. We provide a linear time algorithm computing a PMO and the corresponding generators of the maximal cliques and minimal separators of the complement graph. On a non-chordal graph, the algorithm MLSM, a graph search algorithm computing an MEO and a minimal triangulation of the graph, is used to compute an atom tree of the clique minimal separator decomposition of any graph. View Full-Text
Share & Cite This Article
Berry, A.; Simonet, G. Computing a Clique Tree with the Algorithm Maximal Label Search. Algorithms 2017, 10, 20.
Berry A, Simonet G. Computing a Clique Tree with the Algorithm Maximal Label Search. Algorithms. 2017; 10(1):20.Chicago/Turabian Style
Berry, Anne; Simonet, Geneviève. 2017. "Computing a Clique Tree with the Algorithm Maximal Label Search." Algorithms 10, no. 1: 20.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.