Computing $\vec{\mathcal{S}}$-DAGs and Parity Games

Fuente: arXiv
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Main Authors: Hatzel, Meike, Schröder, Johannes
Format: Preprint
Published: 2024
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author Hatzel, Meike
Schröder, Johannes
author_facet Hatzel, Meike
Schröder, Johannes
contents Treewidth on undirected graphs is known to have many algorithmic applications. When considering directed width-measures there are much less results on their deployment for algorithmic results. In 2022 the first author, Rabinovich and Wiederrecht introduced a new directed width measure, $\vec{\mathcal{S}}$-DAG-width, using directed separations and obtained a structural duality for it. In 2012 Berwanger~et~al.~solved Parity Games in polynomial time on digraphs of bounded DAG-width. With generalising this result to digraphs of bounded $\vec{\mathcal{S}}$-DAG-width and also providing an algorithm to compute the $\vec{\mathcal{S}}$-DAG-width of a given digraphs we give first algorithmical results for this new parameter.
format Preprint
id arxiv_https___arxiv_org_abs_2405_05571
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Computing $\vec{\mathcal{S}}$-DAGs and Parity Games
Hatzel, Meike
Schröder, Johannes
Combinatorics
Discrete Mathematics
Treewidth on undirected graphs is known to have many algorithmic applications. When considering directed width-measures there are much less results on their deployment for algorithmic results. In 2022 the first author, Rabinovich and Wiederrecht introduced a new directed width measure, $\vec{\mathcal{S}}$-DAG-width, using directed separations and obtained a structural duality for it. In 2012 Berwanger~et~al.~solved Parity Games in polynomial time on digraphs of bounded DAG-width. With generalising this result to digraphs of bounded $\vec{\mathcal{S}}$-DAG-width and also providing an algorithm to compute the $\vec{\mathcal{S}}$-DAG-width of a given digraphs we give first algorithmical results for this new parameter.
title Computing $\vec{\mathcal{S}}$-DAGs and Parity Games
topic Combinatorics
Discrete Mathematics
url https://arxiv.org/abs/2405.05571