The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Elimination structures for unsymmetric sparse LU factors
SIAM Journal on Matrix Analysis and Applications
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Approximating treewidth, pathwidth, frontsize, and shortest elimination tree
Journal of Algorithms
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
Journal of Combinatorial Theory Series B
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Journal of Combinatorial Theory Series B
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
DAG-width: connectivity measure for directed graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
On exact algorithms for treewidth
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Journal of Combinatorial Theory Series B
Digraph measures: Kelly decompositions, games, and orderings
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Efficient exact algorithms on planar graphs: exploiting sphere cut branch decompositions
ESA'05 Proceedings of the 13th annual European conference on Algorithms
D-Width: a more natural measure for directed tree width
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Bounded treewidth as a key to tractability of knowledge representation and reasoning
Artificial Intelligence
New Results on the Complexity of Oriented Colouring on Restricted Digraph Classes
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Tractable database design and datalog abduction through bounded treewidth
Information Systems
Recognizing digraphs of Kelly-width 2
Discrete Applied Mathematics
Complexity of semi-stable and stage semantics in argumentation frameworks
Information Processing Letters
Pure Nash equilibria: complete characterization of hard and easy graphical games
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Digraph decompositions and monotonicity in digraph searching
Theoretical Computer Science
Directed nowhere dense classes of graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Towards fixed-parameter tractable algorithms for abstract argumentation
Artificial Intelligence
The dag-width of directed graphs
Journal of Combinatorial Theory Series B
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
Parity games on undirected graphs
Information Processing Letters
Entanglement and the complexity of directed graphs
Theoretical Computer Science
Theoretical Computer Science
A trichotomy for regular simple path queries on graphs
Proceedings of the 32nd symposium on Principles of database systems
The complexity of optimal monotonic planning: the bad, the good, and the causal graph
Journal of Artificial Intelligence Research
Digraph width measures in parameterized algorithmics
Discrete Applied Mathematics
Digraphs of bounded elimination width
Discrete Applied Mathematics
| Hi-index | 5.23 |
We consider various well-known, equivalent complexity measures for graphs such as elimination orderings, k-trees and cops and robber games and study their natural translations to digraphs. We show that on digraphs the translations of these measures are also equivalent and induce a natural connectivity measure. We introduce a decomposition for digraphs and an associated width, Kelly-width, which is equivalent to the aforementioned measure. We demonstrate its usefulness by exhibiting potential applications including polynomial-time algorithms for NP-complete problems on graphs of bounded Kelly-width, and complexity analysis of asymmetric matrix factorization. Finally, we compare the new width to other known decompositions of digraphs.