License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2023.33
URN: urn:nbn:de:0030-drops-174942
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17494/
Staniszewski, Konrad
Parity Games of Bounded Tree-Depth
Abstract
The exact complexity of solving parity games is a major open problem. Several authors have searched for efficient algorithms over specific classes of graphs. In particular, Obdržálek showed that for graphs of bounded tree-width or clique-width, the problem is in P, which was later improved by Ganardi, who showed that it is even in LOGCFL (with an additional assumption for clique-width case). Here we extend this line of research by showing that for graphs of bounded tree-depth the problem of solving parity games is in logspace uniform AC⁰. We achieve this by first considering a parameter that we obtain from a modification of clique-width, which we call shallow clique-width. We subsequently provide a suitable reduction.
BibTeX - Entry
@InProceedings{staniszewski:LIPIcs.CSL.2023.33,
author = {Staniszewski, Konrad},
title = {{Parity Games of Bounded Tree-Depth}},
booktitle = {31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
pages = {33:1--33:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-264-8},
ISSN = {1868-8969},
year = {2023},
volume = {252},
editor = {Klin, Bartek and Pimentel, Elaine},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/17494},
URN = {urn:nbn:de:0030-drops-174942},
doi = {10.4230/LIPIcs.CSL.2023.33},
annote = {Keywords: Parity Games, Circuits, Tree-Depth, Clique-Width}
}
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Keywords: |
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Parity Games, Circuits, Tree-Depth, Clique-Width |
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Collection: |
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31st EACSL Annual Conference on Computer Science Logic (CSL 2023) |
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Issue Date: |
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2023 |
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Date of publication: |
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01.02.2023 |
