# Time and Parallelizability Results for Parity Games with Bounded Treewidth

@inproceedings{Fearnley2012TimeAP, title={Time and Parallelizability Results for Parity Games with Bounded Treewidth}, author={John Fearnley and Sven Schewe}, booktitle={ICALP}, year={2012} }

Parity games are a much researched class of games in NP ∩ CoNP that are not known to be in P. Consequently, researchers have considered specialised algorithms for the case where certain graph parameters are small. In this paper, we show that, if a tree decomposition is provided, then parity games with bounded treewidth can be solved in O(k3k+2 ·n2 ·(d+1)3k) time, where n, k, and d are the size, treewidth, and number of priorities in the parity game. This significantly improves over previously…

## 11 Citations

### Parity Games of Bounded Tree- and Clique-Width

- Computer ScienceFoSSaCS
- 2015

It is shown that deciding the winner of a parity game is in LogCFL, if the underlying graph has bounded tree-width, and in LogDCFL, and it is proven that parity games of bounded clique-width can be solved in logCFL via a log-space reduction to the bounded tree's width case.

### Solving parity games via priority promotion

- Computer ScienceCAV
- 2016

A new algorithm is proposed for the solution of this decision problem, based on the idea of promoting vertexes to higher priorities during the search for winning regions, exhibiting the best space complexity among the currently known solutions.

### New Deterministic Algorithms for Solving Parity Games

- Computer ScienceLATIN
- 2016

A fixed-parameter algorithm that solves bipartite parity games in time \(k^{O(\sqrt{k})}\cdot O(n^3)\) and general parityGames in time p-m where p denotes the number of distinct priorities and m denotes thenumber of edges.

### Parity Games, Imperfect Information and Structural Complexity

- Computer ScienceArXiv
- 2017

A simple method is used to measure the amount of "unawareness"' of a player, and it turns out that if it is unbounded, low structural complexity does not make the problem simpler, it remains EXPTIME-hard or PSPACE-hard even on very simple graphs.

### Graph operations on parity games and polynomial-time algorithms

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 2016

### Faster Algorithms for Markov Decision Processes with Low Treewidth

- Computer Science, MathematicsCAV
- 2013

Two improved static algorithms are presented for both the maximal end-component decomposition and the almost-sure reachability set computation for Markov decision processes (MDPs) for MDPs with treewidth k that run in amortized logarithmic time.

### Graph complexity measures and monotonicity

- Mathematics
- 2013

A weak variant of monotonicity is proved for two cops, a property of winning cop strategies, which implies the existence of suitable decompositions of the given graphs which allow for efficient algorithms for difficult computational problems.

### DAG-width of Control Flow Graphs with Applications to Model Checking

- Mathematics, Computer ScienceArXiv
- 2015

One consequence of this result is that parity games (and hence the $\mu$-calculus model checking problem), which are known to be tractable on graphs of bounded DAG-width, can be solved efficiently in practice on control flow graphs.

### Parity games, separations, and the modal μ-calculus

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- 2017

This dissertation aims to provide a history of web exceptionalism from 1989 to 2002, a period chosen in order to explore its roots as well as specific cases up to and including the year in which descriptions of “Web 2.0” began to circulate.

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