منابع مشابه
Vertical Decomposition of a Lattice Using Clique Separators
A concept (or Galois) lattice is built on a binary relation; this relation can be represented by a bipartite graph. We explain how we can use the graph tool of clique minimal separator decomposition to decompose some bipartite graphs into subgraphs in linear time; each subgraph corresponds to a subrelation. We show that the lattices of these subrelations easily yield the lattice of the global r...
متن کاملDecomposition by maxclique separators
We provide a minimal counterexample to the correctness of an algorithm proposed by R. Tarjan for decomposing a graph by maximal clique separators. We also suggest a modification to that algorithm which not only corrects it but also retains its O(nm) time complexity.
متن کاملClique-decomposition revisited
The decomposition of graphs by clique-minimal separators is a common algorithmic tool, first introduced by Tarjan. Since it allows to cut a graph into smaller pieces, it can be applied to preprocess the graphs in the computation of many optimization problems. However, the best known clique-decomposition algorithms have respective O(nm)-time and O(n)-time complexity, that is prohibitive for larg...
متن کاملNear-Optimal Separators in String Graphs
Let G be a string graph (an intersection graph of continuous arcs in the plane) with m edges. Fox and Pach proved that G has a separator consisting of O(m √ logm) vertices, and they conjectured that the bound of O( √ m) actually holds. We obtain separators with O( √ m logm) vertices. Let G = (V,E) be a graph with n vertices. A separator in G is a set S ⊆ V of vertices such that there is a parti...
متن کاملAn Introduction to Clique Minimal Separator Decomposition
This paper is a review which presents and explains the decomposition by clique minimal separators, which is a promising tool for representing and decomposing experimental data. The pace is leisurely, we give many examples and figures. Easy algorithms are provided to implement this decomposition. The historical and theoretical background is given, as well as sketches of proofs of the structural ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1993
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90510-z