Next Article in Journal
Concurrent vs. Exclusive Reading in Parallel Decoding of LZ-Compressed Files
Previous Article in Journal
Pressure Control for a Hydraulic Cylinder Based on a Self-Tuning PID Controller Optimized by a Hybrid Optimization Algorithm
Article Menu

Export Article

Open AccessArticle
Algorithms 2017, 10(1), 20; doi:10.3390/a10010020

Computing a Clique Tree with the Algorithm Maximal Label Search

LIMOS (Laboratoire d’Informatique, d’Optimisation et de Modélisation des Systèmes) UMR CNRS 6158, Ensemble Scientifique des Cézeaux, F-63178 Aubière CEDEX, France
LIRMM (Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier), 161 Rue Ada, F-34095 Montpellier CEDEX 5, France
Author to whom correspondence should be addressed.
Academic Editor: Qianping Gu
Received: 29 October 2016 / Revised: 12 January 2017 / Accepted: 16 January 2017 / Published: 25 January 2017
View Full-Text   |   Download PDF [311 KB, uploaded 25 January 2017]   |  


The 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
Keywords: chordal graph; clique tree; perfect elimination ordering; perfect moplex ordering; Maximal Label Search; LexBFS; MCS chordal graph; clique tree; perfect elimination ordering; perfect moplex ordering; Maximal Label Search; LexBFS; MCS

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Berry, A.; Simonet, G. Computing a Clique Tree with the Algorithm Maximal Label Search. Algorithms 2017, 10, 20.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Algorithms EISSN 1999-4893 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top