Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
Journal of Combinatorial Theory Series B
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Tree-depth, subgraph coloring and homomorphism bounds
European Journal of Combinatorics
Vertex disjoint paths on clique-width bounded graphs
Theoretical Computer Science
Journal of Combinatorial Theory Series B
Digraph measures: Kelly decompositions, games, and orderings
Theoretical Computer Science
Finding Branch-Decompositions and Rank-Decompositions
SIAM Journal on Computing
A fixed-parameter algorithm for the directed feedback vertex set problem
Journal of the ACM (JACM)
A New Algorithm for Finding Trees with Many Leaves
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Communication: On complexity of Minimum Leaf Out-Branching problem
Discrete Applied Mathematics
Minimum leaf out-branching and related problems
Theoretical Computer Science
Disjoint directed and undirected paths and cycles in digraphs
Theoretical Computer Science
On parse trees and Myhill-Nerode-type tools for handling graphs of bounded rank-width
Discrete Applied Mathematics
Algorithmic lower bounds for problems parameterized by clique-width
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Intractability of Clique-Width Parameterizations
SIAM Journal on Computing
Parameterized Tractability of Edge-Disjoint Paths on Directed Acyclic Graphs
SIAM Journal on Discrete Mathematics
Digraph decompositions and monotonicity in digraph searching
Theoretical Computer Science
Oriented coloring: complexity and approximation
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
D-Width: a more natural measure for directed tree width
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
The dag-width of directed graphs
Journal of Combinatorial Theory Series B
On the algorithmic effectiveness of digraph decompositions and complexity measures
Discrete Optimization
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
A unified approach to polynomial algorithms on graphs of bounded (bi-)rank-width
European Journal of Combinatorics
The Rank-Width of Edge-Coloured Graphs
Theory of Computing Systems
Combinatorial Optimization on Graphs of Bounded Treewidth
The Computer Journal
Width Parameters Beyond Tree-width and their Applications
The Computer Journal
| Hi-index | 0.04 |
In contrast to undirected width measures such as tree-width, which have provided many important algorithmic applications, analogous measures for digraphs such as directed tree-width or DAG-width do not seem so successful. Several recent papers have given some evidence on the negative side. We confirm and consolidate this overall picture by thoroughly and exhaustively studying the complexity of a range of directed problems with respect to various parameters, and by showing that they often remain NP-hard even on graph classes that are restricted very beyond having small DAG-width. On the positive side, it turns out that clique-width (of digraphs) performs much better on virtually all considered problems, from the parameterized complexity point of view.