Organizing the atoms of the clique separator decomposition into an atom tree
نویسندگان
چکیده
We define an atom tree of a graph as a generalization of a clique tree: its nodes are the atoms obtained by clique minimal separator decomposition, and its edges correspond to the clique minimal separators of the
منابع مشابه
Efficient clique decomposition of a graph into its atom graph
We explain how to organize the atoms resulting from clique minimal separator decomposition into a metagraph which we call the atom graph, and give an efficient recursive algorithm to compute this graph at no extra cost than computing the atoms.
متن کاملDécomposition par séparateurs minimaux complets et applications
We worked on clique minimal separator decomposition. In order to compute this decomposition on a graph G we need to compute the minimal separators of its triangulation H. In this context, the first efforts were on finding a clique minimal separators in a chordal graph. We defined a structure called atom tree inspired from the clique tree to compute and represent the final products of the decomp...
متن کاملNew Applications of Clique Separator Decomposition for the Maximum Weight Stable Set Problem
Graph decompositions such as decomposition by clique separators and modular decomposition are of crucial importance for designing efficient graph algorithms. Clique separators in graphs were used by Tarjan as a divide-and-conquer approach for solving various problems such as the Maximum Weight Stable Set (MWS) problem, Colouring and Minimum Fill-in. The basic tool is a decomposition tree of the...
متن کاملGraph Decomposition Approaches for Terminology Graphs
We propose a graph-based decomposition methodology of a network of document features represented by a terminology graph. The graph is automatically extracted from raw data based on Natural Language Processing techniques implemented in the TermWatch system. These graphs are Small Worlds. Based on clique minimal separators and the associated graph of atoms: a subgraph without clique separator, we...
متن کاملClique Separator Decomposition of Hole- and Diamond-Free Graphs and Algorithmic Consequences
Clique separator decomposition introduced by Tarjan and Whitesides is one of the most important graph decompositions. A graph is an atom if it has no clique separator. A hole is a chordless cycle with at least five vertices, and an antihole is the complement graph of a hole. A graph is weakly chordal if it is holeand antihole-free. K4−e is also called diamond. Paraglider has five vertices four ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Applied Mathematics
دوره 177 شماره
صفحات -
تاریخ انتشار 2014