---
_id: '2246'
abstract:
- lang: eng
text: 'Muller games are played by two players moving a token along a graph; the
winner is determined by the set of vertices that occur infinitely often. The central
algorithmic problem is to compute the winning regions for the players. Different
classes and representations of Muller games lead to problems of varying computational
complexity. One such class are parity games; these are of particular significance
in computational complexity, as they remain one of the few combinatorial problems
known to be in NP ∩ co-NP but not known to be in P. We show that winning regions
for a Muller game can be determined from the alternating structure of its traps.
To every Muller game we then associate a natural number that we call its trap
depth; this parameter measures how complicated the trap structure is. We present
algorithms for parity games that run in polynomial time for graphs of bounded
trap depth, and in general run in time exponential in the trap depth. '
author:
- first_name: Andrey
full_name: Grinshpun, Andrey
last_name: Grinshpun
- first_name: Pakawat
full_name: Phalitnonkiat, Pakawat
last_name: Phalitnonkiat
- first_name: Sasha
full_name: Rubin, Sasha
id: 2EC51194-F248-11E8-B48F-1D18A9856A87
last_name: Rubin
- first_name: Andrei
full_name: Tarfulea, Andrei
last_name: Tarfulea
citation:
ama: Grinshpun A, Phalitnonkiat P, Rubin S, Tarfulea A. Alternating traps in Muller
and parity games. Theoretical Computer Science. 2014;521:73-91. doi:10.1016/j.tcs.2013.11.032
apa: Grinshpun, A., Phalitnonkiat, P., Rubin, S., & Tarfulea, A. (2014). Alternating
traps in Muller and parity games. Theoretical Computer Science. Elsevier.
https://doi.org/10.1016/j.tcs.2013.11.032
chicago: Grinshpun, Andrey, Pakawat Phalitnonkiat, Sasha Rubin, and Andrei Tarfulea.
“Alternating Traps in Muller and Parity Games.” Theoretical Computer Science.
Elsevier, 2014. https://doi.org/10.1016/j.tcs.2013.11.032.
ieee: A. Grinshpun, P. Phalitnonkiat, S. Rubin, and A. Tarfulea, “Alternating traps
in Muller and parity games,” Theoretical Computer Science, vol. 521. Elsevier,
pp. 73–91, 2014.
ista: Grinshpun A, Phalitnonkiat P, Rubin S, Tarfulea A. 2014. Alternating traps
in Muller and parity games. Theoretical Computer Science. 521, 73–91.
mla: Grinshpun, Andrey, et al. “Alternating Traps in Muller and Parity Games.” Theoretical
Computer Science, vol. 521, Elsevier, 2014, pp. 73–91, doi:10.1016/j.tcs.2013.11.032.
short: A. Grinshpun, P. Phalitnonkiat, S. Rubin, A. Tarfulea, Theoretical Computer
Science 521 (2014) 73–91.
date_created: 2018-12-11T11:56:33Z
date_published: 2014-02-13T00:00:00Z
date_updated: 2021-01-12T06:56:16Z
day: '13'
department:
- _id: KrCh
doi: 10.1016/j.tcs.2013.11.032
intvolume: ' 521'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1303.3777
month: '02'
oa: 1
oa_version: Submitted Version
page: 73 - 91
publication: Theoretical Computer Science
publication_identifier:
issn:
- '03043975'
publication_status: published
publisher: Elsevier
publist_id: '4703'
quality_controlled: '1'
scopus_import: 1
status: public
title: Alternating traps in Muller and parity games
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 521
year: '2014'
...