Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
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
D-Width: a more natural measure for directed tree width
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Digraph measures: Kelly decompositions, games, and orderings
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
Monotonicity of non-deterministic graph searching
Theoretical Computer Science
Digraph measures: Kelly decompositions, games, and orderings
Theoretical Computer Science
Digraph searching, directed vertex separation and directed pathwidth
Discrete Applied Mathematics
Finite Automata, Digraph Connectivity, and Regular Expression Size
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
The Descriptive Complexity of Parity Games
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
An Optimal Strategy Improvement Algorithm for Solving Parity and Payoff Games
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Polynomial-Time Under-Approximation of Winning Regions in Parity Games
Electronic Notes in Theoretical Computer Science (ENTCS)
Digraph Decompositions and Monotonicity in Digraph Searching
Graph-Theoretic Concepts in Computer Science
Communication: On complexity of Minimum Leaf Out-Branching problem
Discrete Applied Mathematics
Bounded treewidth as a key to tractability of knowledge representation and reasoning
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
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
Directed searching digraphs: monotonicity and complexity
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Monotonicity of non-deterministic graph searching
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Characterization and recognition of digraphs of bounded Kelly-width
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Solving parity games in big steps
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Undirected graphs of entanglement 2
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Directed graphs of entanglement two
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
The complexity of Nash equilibria in infinite multiplayer games
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Parity games with partial information played on graphs of bounded complexity
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Digraph decompositions and monotonicity in digraph searching
Theoretical Computer Science
LIFO-search on digraphs: a searching game for cycle-rank
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Directed nowhere dense classes of graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A polynomial time algorithm for bounded directed pathwidth
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
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
LIFO-search: A min-max theorem and a searching game for cycle-rank and tree-depth
Discrete Applied Mathematics
Time and parallelizability results for parity games with bounded treewidth
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Parity games on undirected graphs
Information Processing Letters
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
The power of counting logics on restricted classes of finite structures
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 cure for stuttering parity games
ICTAC'12 Proceedings of the 9th international conference on Theoretical Aspects of Computing
The rabin index of parity games
HVC'11 Proceedings of the 7th international Haifa Verification conference on Hardware and Software: verification and testing
Fatal attractors in parity games
FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
Alternating traps in Muller and parity games
Theoretical Computer Science
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 development. Tree-width is characterised by a game known as the cops-and-robber game where a number of cops chase a robber on the graph. We consider the natural adaptation of this game to directed graphs and show that monotone strategies in the game yield a measure with an associated notion of graph decomposition that can be seen to describe how close a directed graph is to a directed acyclic graph (DAG). This promises to be useful in 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 measures such as entanglement and directed tree-width. One 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.