Theoretical Computer Science
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
Journal of the ACM (JACM)
Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
On model checking for the &mgr;-calculus and its fragments
Theoretical Computer Science
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
DAG-width: connectivity measure for directed graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Journal of Combinatorial Theory Series B
Digraph measures: Kelly decompositions, games, and orderings
Theoretical Computer Science
The complexity of tree automata and logics of programs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Digraph Decompositions and Monotonicity in Digraph Searching
Graph-Theoretic Concepts in Computer Science
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects 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
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Entanglement and the complexity of directed graphs
Theoretical Computer Science
A trichotomy for regular simple path queries on graphs
Proceedings of the 32nd symposium on Principles of database systems
Faster algorithms for markov decision processes with low treewidth
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Beyond bidimensionality: Parameterized subexponential algorithms on directed graphs
Information and Computation
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
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Tree-width is a well-known metric on undirected graphs that measures how tree-like a graph is and gives a notion of graph decomposition that proves useful in algorithm design. Tree-width can be characterised by a graph searching game where a number of cops attempt to capture a robber. We consider the natural adaptation of this game to directed graphs and show that monotone strategies in the game yield a measure, called dag-width, that can be seen to describe how close a directed graph is to a directed acyclic graph (dag). We also provide an associated decomposition and show how it is useful for developing algorithms on directed graphs. In particular, we show that the problem of determining the winner of a parity game is solvable in polynomial time on graphs of bounded dag-width. We also consider the relationship between dag-width and other connectivity measures such as directed tree-width and path-width. A consequence we obtain is that certain NP-complete problems such as Hamiltonicity and disjoint paths are polynomial-time computable on graphs of bounded dag-width.