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Errata for: A subexponential lower bound for the Random Facet algorithm for Parity Games
[article]
2014
arXiv
pre-print
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We then obtained a lower bound on the expected number of pivoting steps performed by Random-Facet^* and claimed that the same lower bound holds also for Random-Facet. ...
number of pivoting steps performed by Random-Facet^*, a variant of Random-Facet that bases its random decisions on one random permutation. ...
The Random-Facet * algorithm is identical to the Random-Facet algorithm, except that it takes as an additional argument a permutation σ : E → {1, . . . , |E|} of the edges and always removes the first ...
arXiv:1410.7871v1
fatcat:dlj3nlyqwjfmlodj7ffpgxnpaq
Strategy Improvement and Randomized Subexponential Algorithms for Stochastic Parity Games
[chapter]
2006
Lecture Notes in Computer Science
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From the strategy improvement algorithm we obtain a randomized subexponential-time algorithm to solve such games. ...
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. ...
[1] used the strategy improvement scheme to derive a randomized subexponential-time algorithm for 2-player parity games. And recently, Jurdziński et al. ...
doi:10.1007/11672142_42
fatcat:2bbrt674tfhr3jchbjgm63mwnq
A subexponential lower bound for the Random Facet algorithm for Parity Games
[chapter]
2011
Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms
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The currently theoretically fastest algorithms for the solution of all these games are adaptations of the randomized algorithms of Kalai and of Matoušek, Sharir and Welzl for LP-type problems, an abstract ...
We show, that this, unfortunately, is not the case by constructing explicit parity games on which the expected running time of the Random Facet algorithm is close to the subexponential upper bound. ...
Another natural randomized algorithm for solving parity games and other games is the RandomEdge algorithm in which a random improving switch is performed at each step. ...
doi:10.1137/1.9781611973082.19
dblp:conf/soda/FriedmannHZ11
fatcat:faoxjfsoi5culirk2nlaghs7uy
A Combinatorial Strongly Subexponential Strategy Improvement Algorithm for Mean Payoff Games
[chapter]
2004
Lecture Notes in Computer Science
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We suggest the first strongly subexponential and purely combinatorial algorithm for mean payoff games. It is based on solving a new "controlled" version of the shortest paths problem. ...
All previous algorithms for mean payoff games were either exponential or pseudopolynomial (which is purely exponential for exponentially large edge weights). ...
We thank DIMACS for providing a creative working environment. We are grateful to Leonid Khachiyan, Vladimir Gurvich, and Endre Boros for inspiring discussions and illuminating ideas. ...
doi:10.1007/978-3-540-28629-5_52
fatcat:hr4xubsmr5cwpluitusvvopedu
A deterministic subexponential algorithm for solving parity games
2006
Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06
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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
2008
SIAM journal on computing (Print)
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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
A Discrete Subexponential Algorithm for Parity Games
[chapter]
2003
Lecture Notes in Computer Science
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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
Page 9262 of Mathematical Reviews Vol. , Issue 2002M
[page]
2002
Mathematical Reviews
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(S-UPPS-CS; Uppsala)
A randomized subexponential algorithm for parity games. (English summary)
Twelfth Nordic Workshop on Programming Theory (Bergen, 2000).
Nordic J. ...
The present authors propose a randomized algorithm which, in the case when the number of colors is sufficiently big with respect to the game size, solves the problem in subexponential time, over- coming ...
Combinatorial structure and randomized subexponential algorithms for infinite games
2005
Theoretical Computer Science
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In this setting, we suggest randomized subexponential algorithms appropriate for RLG-and PRLG-function optimization. ...
We show that the subexponential algorithms for combinatorial linear programming, due to Kalai and Matoušek, Sharir, Welzl, can be adapted for optimizing the RLG-and PRLG-functions. ...
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 environment. ...
doi:10.1016/j.tcs.2005.07.041
fatcat:u3gsujjxkjflzfu5ndcr6cgqru
Complexity of Model Checking by Iterative Improvement: The Pseudo-Boolean Framework
[chapter]
2004
Lecture Notes in Computer Science
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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 ...
Later we succeeded to generalize and adapt those subexponential schemes to create a discrete subexponential algorithm for general (non-binary) parity games [5] , and extend it to combinatorial structures ...
doi:10.1007/978-3-540-39866-0_38
fatcat:cczswhsgvratdlq6pi7tubgkva
A combinatorial strongly subexponential strategy improvement algorithm for mean payoff games
2007
Discrete Applied Mathematics
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We suggest the first strongly subexponential and purely combinatorial algorithm for solving the mean payoff games problem. ...
This allows us to construct a randomized algorithm of complexity min(poly·W, 2 O( √ n log n) ), which is simultaneously pseudopolynomial (W is the maximal absolute edge weight) and subexponential in the ...
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
A Subexponential Lower Bound for Zadeh's Pivoting Rule for Solving Linear Programs and Games
[chapter]
2011
Lecture Notes in Computer Science
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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
Cyclic games and linear programming
2008
Discrete Applied Mathematics
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The latter provides a nice unifying formulation subsuming (being "hard" for) a class of games in NP ∩ coNP. ...
(Sections 4,6, and 8), providing new algorithms, often more efficient than previously known (e.g., subexponential; cf., Section 8). ...
Subexponential algorithms for parity games The described randomized subexponential and simultaneously pseudopolynomial algorithm for MPGs (Corollary 8.10) immediately gives the algorithm for parity games ...
doi:10.1016/j.dam.2008.04.012
fatcat:5fmgypimu5cs3ahclgd4lsc4si
Solving Random Parity Games in Polynomial Time
[article]
2020
arXiv
pre-print
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We consider the problem of solving random parity games. ...
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 ...
payoff games and running in subexponential expected time 2 O(c 1/(1+2 ) ) for a "large" number of colors c = Ω(|V| 1/2+ ), 0 < ≤ 1/2. [3] inspires from [34] and proposes a randomized algorithm with ...
arXiv:2007.08387v1
fatcat:ybur6jrpvjfgrn4z3l6vphucj4
Simple Stochastic Games, Parity Games, Mean Payoff Games and Discounted Payoff Games Are All LP-Type Problems
2007
Algorithmica
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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
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