Theory of 2-structures. Part I: clans, basic subclasses, and morphisms
Theoretical Computer Science
Theory of 2-structures. Part II: representation through labeled tree families
Theoretical Computer Science
Introduction to algorithms
k-NLC graphs and polynomial algorithms
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Modular decomposition of graphs and two-structures
Modular decomposition of graphs and two-structures
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Linear Time Solvable Optimization Problems on Graphs of Bounded Clique Width
WG '98 Proceedings of the 24th International Workshop on Graph-Theoretic Concepts in Computer Science
The Tree-Width of Clique-Width Bounded Graphs Without Kn, n
WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
How to Solve NP-hard Graph Problems on Clique-Width Bounded Graphs in Polynomial Time
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
log n-Approximative NLCk-Decomposition in O(n2k+1) Time
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
| Hi-index | 0.00 |
NLCk is a family of algebras on vertex-labeled graphs introduced by Wanke. An NLC-decomposition of a graph is a derivation of this graph from single vertices using the operations in question. The width of the decomposition is the number of labels used, and the NLC-width of the graph is the smallest width among its NLC-decompositions. Many difficult graph problems can be solved efficiently with dynamic programming if an NLC-decomposition of low width is given for the input graph. It is unknown though whether arbitrary graphs of NLC-width at most k can be decomposed with k labels in polynomial time. So far this has been possible only for k = 1, which corresponds to cographs. In this paper, an algorithm is presented that works for k = 2. It runs in O(n4 log n) time and uses O(n2) space. Related concepts: clique-decomposition, cliquewidth.