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A deterministic subexponential algorithm for solving parity games

Marcin Jurdziński, Mike Paterson, Uri Zwick
2006 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06  
We use a completely different, and elementary, approach to obtain a deterministic subexponential algorithm for the solution of parity games.  ...  The existence of polynomial time algorithms for the solution of parity games is a major open problem.  ...  We thank a SODA'06 referee for suggestions that resulted in a significant simplification of the proofs of Theorems 8.1 and 8.2, and the Journal referees whose comments helped us improve the presentation  ... 
doi:10.1145/1109557.1109571 fatcat:ra2bysahajbyzigah3aa6o6sum

A Deterministic Subexponential Algorithm for Solving Parity Games

Marcin Jurdziński, Mike Paterson, Uri Zwick
2008 SIAM journal on computing (Print)  
We use a completely different, and elementary, approach to obtain a deterministic subexponential algorithm for the solution of parity games.  ...  The existence of polynomial time algorithms for the solution of parity games is a major open problem.  ...  We thank a SODA'06 referee for suggestions that resulted in a significant simplification of the proofs of Theorems 8.1 and 8.2, and the Journal referees whose comments helped us improve the presentation  ... 
doi:10.1137/070686652 fatcat:tjdeb53k65cr5lhrymlmmdyz4q

Page 9262 of Mathematical Reviews Vol. , Issue 2002M [page]

2002 Mathematical Reviews  
(S-UPPS-CS; Uppsala) A randomized subexponential algorithm for parity games. (English summary) Twelfth Nordic Workshop on Programming Theory (Bergen, 2000). Nordic J.  ...  Solving parity games is an algorithmic problem whose exact com- plexity is unknown and has recently attracted much attention.  ... 

A subexponential lower bound for the Random Facet algorithm for Parity Games [chapter]

Oliver Friedmann, Thomas Dueholm Hansen, Uri Zwick
2011 Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms  
It is a major open problem whether these game families can be solved in polynomial time.  ...  They also form a very natural subclass of Deterministic Mean Payoff Games, which in turn is a very natural subclass of turn-based Stochastic Mean Payoff Games.  ...  No such deterministic subexponential algorithms are known for the more general classes of deterministic or stochastic mean payoff games.  ... 
doi:10.1137/1.9781611973082.19 dblp:conf/soda/FriedmannHZ11 fatcat:faoxjfsoi5culirk2nlaghs7uy

Strategy Improvement and Randomized Subexponential Algorithms for Stochastic Parity Games [chapter]

Krishnendu Chatterjee, Thomas A. Henzinger
2006 Lecture Notes in Computer Science  
These games lie in NP ∩ coNP. We present a strategy improvement algorithm for stochastic parity games; this is the first non-brute-force algorithm for solving these games.  ...  From the strategy improvement algorithm we obtain a randomized subexponential-time algorithm to solve such games.  ...  [9] found a deterministic subexponential-time algorithm for 2-player parity games.  ... 
doi:10.1007/11672142_42 fatcat:2bbrt674tfhr3jchbjgm63mwnq

A survey of stochastic ω-regular games

Krishnendu Chatterjee, Thomas A. Henzinger
2012 Journal of computer and system sciences (Print)  
Important distinctions are whether a graph game is turn-based or concurrent; deterministic or stochastic; zero-sum or not.  ...  We summarize classical and recent results about two-player games played on graphs with ω-regular objectives. These games have applications in the verification and synthesis of reactive systems.  ...  [64] gave a deterministic subexponential-time algorithm for solving 2-player games with parity objectives. Algorithms for 2 1 2 -player reachability games.  ... 
doi:10.1016/j.jcss.2011.05.002 fatcat:267iudbahzf4tdef2fo573l3ie

A Subexponential Lower Bound for Zadeh's Pivoting Rule for Solving Linear Programs and Games [chapter]

Oliver Friedmann
2011 Lecture Notes in Computer Science  
We start by building 2-player parity games (PGs) on which the policy iteration with the Least-Entered rule performs a subexponential number of iterations.  ...  The simplex algorithm is among the most widely used algorithms for solving linear programs in practice.  ...  I would like to thank Uri Zwick and Thomas Dueholm Hansen for pointing me to this challenging pivoting rule and for numerous inspiring discussions on the subject.  ... 
doi:10.1007/978-3-642-20807-2_16 fatcat:6umv2rzbxrgcpdgkojtvdc43ki

A Discrete Subexponential Algorithm for Parity Games [chapter]

Henrik Björklund, Sven Sandberg, Sergei Vorobyov
2003 Lecture Notes in Computer Science  
We suggest a new randomized algorithm for solving parity games with worst case time complexity roughly min " O  ...  The authors thank anonymous STACS'2003 referees for constructive remarks and suggestions towards improvement of the paper.  ...  A different subexponential algorithm for parity games is described in [5] . Outline.  ... 
doi:10.1007/3-540-36494-3_58 fatcat:szthswm2jnenhepgvxtkgnr4zi

A combinatorial strongly subexponential strategy improvement algorithm for mean payoff games

Henrik Björklund, Sergei Vorobyov
2007 Discrete Applied Mathematics  
We suggest the first strongly subexponential and purely combinatorial algorithm for solving the mean payoff games problem.  ...  Mean payoff games are easily reducible to this problem. We suggest an algorithm for computing longest shortest paths.  ...  Acknowledgments We are grateful to Leonid Khachiyan, Vladimir Gurvich, and Endre Boros for inspiring discussions and illuminating ideas. We thank DIMACS for providing a creative working environment.  ... 
doi:10.1016/j.dam.2006.04.029 fatcat:6ecob37j55dz7mo4hn43fg6cse

Complexity of Model Checking by Iterative Improvement: The Pseudo-Boolean Framework [chapter]

Henrik Björklund, Sven Sandberg, Sergei Vorobyov
2004 Lecture Notes in Computer Science  
no loss of generality, since a game with non-binary choices may be reduced to binary.  ...  Grants "Infinite Games: Algorithms and Complexity" and "Interior-Point Methods for Infinite Games". ⋆⋆ Extended abstract in PSI'03, LNCS 2890, c Springer-Verlag 1 The restriction to two successors is  ...  The fifth algorithm, KLRA, was first proposed in [21] for solving simple stochastic games, with a subexponential upper bound on the expected running time.  ... 
doi:10.1007/978-3-540-39866-0_38 fatcat:cczswhsgvratdlq6pi7tubgkva

Solving Random Parity Games in Polynomial Time [article]

Richard Combes, Mikael Touati
2020 arXiv   pre-print
We prove that parity games exibit a phase transition threshold above d_P, so that when the degree of the graph that defines the game has a degree d > d_P then there exists a polynomial time algorithm that  ...  We consider the problem of solving random parity games.  ...  This complexity was also achieved by subexponential polynomial space deterministic algorithm [ [43] shows a new strategy improvement algorithm for parity and payoff games with optimal local strategy  ... 
arXiv:2007.08387v1 fatcat:ybur6jrpvjfgrn4z3l6vphucj4

Simple Stochastic Games, Parity Games, Mean Payoff Games and Discounted Payoff Games Are All LP-Type Problems

Nir Halman
2007 Algorithmica  
Using this formulation, and the known algorithm of Sharir and Welzl [SW] for LP-type problems, we obtain the first strongly subexponential solution for SSGs (a strongly subexponential algorithm has only  ...  We also give alternative simple proofs for the best known upper bounds for Parity Games and binary SSGs.  ...  I thank Uri Zwick who brought the paper by Ludwig [L] to my attention, and Leo Ruest for pointing out the reference [GW2] .  ... 
doi:10.1007/s00453-007-0175-3 fatcat:doi75navtvb6lmlxrhmn6cdv5u

New Deterministic Algorithms for Solving Parity Games [chapter]

Matthias Mnich, Heiko Röglin, Clemens Rösner
2016 Lecture Notes in Computer Science  
As a polynomial-time algorithm for solving parity games has remained elusive, researchers have started to consider which restrictions on the game allow for polynomial-time algorithms.  ...  We also obtain novel kernelization results and an improved deterministic algorithm for graphs with small average degree. √ n) for general parity games and of n O( √ n/ log n) for parity games in which  ...  M. thanks Lászlo Végh for introducing him to parity games, and the authors of [8] for sending us a preprint.  ... 
doi:10.1007/978-3-662-49529-2_47 fatcat:f45tjdrsorh35mm3jbgpacqtlu

New Deterministic Algorithms for Solving Parity Games [article]

Matthias Mnich, Heiko Röglin, Clemens Rösner
2015 arXiv   pre-print
Our main result is a fixed-parameter algorithm that solves bipartite parity games in time k^O(√(k))· O(n^3), and general parity games in time (p+k)^O(√(k))· O(pnm), where p is the number of distinct priorities  ...  We also obtain novel kernelization results and an improved deterministic algorithm for graphs with small average degree.  ...  M. thanks Lászlo Végh for introducing him to parity games, and the authors of [8] for sending us a preprint.  ... 
arXiv:1512.03246v1 fatcat:6x2rouc325dgnjug52b7vma5e4

Universal trees grow inside separating automata: Quasi-polynomial lower bounds for parity games [article]

Wojciech Czerwiński, Laure Daviaud, Nathanaël Fijalkow, Marcin Jurdziński, Ranko Lazić, Paweł Parys
2018 arXiv   pre-print
This forms a barrier that all existing approaches must overcome in the ongoing quest for a polynomial-time algorithm for solving parity games.  ...  Several distinct techniques have been proposed to design quasi-polynomial algorithms for solving parity games since the breakthrough result of Calude, Jain, Khoussainov, Li, and Stephan (2017): play summaries  ...  Acknowledgements This research has been supported by the EPSRC grant EP/P020992/1 (Solving Parity Games in Theory and Practice). W. Czerwiński and P.  ... 
arXiv:1807.10546v2 fatcat:t4fhnths5vg47akfoqlkhzmbni
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