New deterministic algorithms for solving parity games

Matthias Mnich; Heiko Roglin; Clemens Rosner

doi:10.1016/j.disopt.2018.06.001

New deterministic algorithms for solving parity games

Matthias Mnich^*, Heiko Roglin, Clemens Rosner

^*Corresponding author for this work

QE Operations research

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We study parity games in which one of the two players controls only a small number k of nodes and the other player controls the n - k other nodes of the game. Our main result is a fixed-parameter algorithm that solves bipartite Parity games in time k(O(root k)) . O(n(3)), and general parity games in time (p + k)(O(root k)) . O(pnm), where p is the number of distinct priorities and m is the number of edges. For all games with k = o(n) this improves the previously fastest algorithm by Jurdzinski, Paterson, and Zwick (SICOMP 2008).

Original language	English
Pages (from-to)	73-95
Number of pages	23
Journal	Discrete Optimization
Volume	30
DOIs	https://doi.org/10.1016/j.disopt.2018.06.001
Publication status	Published - 1 Nov 2018

Keywords

Parity games
Fixed-parameter algorithms
Kernelization
Subexponential algorithms
SUBEXPONENTIAL ALGORITHM
INFINITE GAMES
WIDTH

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title = "New deterministic algorithms for solving parity games",

abstract = "We study parity games in which one of the two players controls only a small number k of nodes and the other player controls the n - k other nodes of the game. Our main result is a fixed-parameter algorithm that solves bipartite Parity games in time k(O(root k)) . O(n(3)), and general parity games in time (p + k)(O(root k)) . O(pnm), where p is the number of distinct priorities and m is the number of edges. For all games with k = o(n) this improves the previously fastest algorithm by Jurdzinski, Paterson, and Zwick (SICOMP 2008).We also obtain novel kernelization results and an improved deterministic algorithm for graphs with small average degree. (C) 2018 Elsevier B.V. All rights reserved.",

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author = "Matthias Mnich and Heiko Roglin and Clemens Rosner",

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T1 - New deterministic algorithms for solving parity games

AU - Mnich, Matthias

AU - Roglin, Heiko

AU - Rosner, Clemens

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Y1 - 2018/11/1

N2 - We study parity games in which one of the two players controls only a small number k of nodes and the other player controls the n - k other nodes of the game. Our main result is a fixed-parameter algorithm that solves bipartite Parity games in time k(O(root k)) . O(n(3)), and general parity games in time (p + k)(O(root k)) . O(pnm), where p is the number of distinct priorities and m is the number of edges. For all games with k = o(n) this improves the previously fastest algorithm by Jurdzinski, Paterson, and Zwick (SICOMP 2008).We also obtain novel kernelization results and an improved deterministic algorithm for graphs with small average degree. (C) 2018 Elsevier B.V. All rights reserved.

AB - We study parity games in which one of the two players controls only a small number k of nodes and the other player controls the n - k other nodes of the game. Our main result is a fixed-parameter algorithm that solves bipartite Parity games in time k(O(root k)) . O(n(3)), and general parity games in time (p + k)(O(root k)) . O(pnm), where p is the number of distinct priorities and m is the number of edges. For all games with k = o(n) this improves the previously fastest algorithm by Jurdzinski, Paterson, and Zwick (SICOMP 2008).We also obtain novel kernelization results and an improved deterministic algorithm for graphs with small average degree. (C) 2018 Elsevier B.V. All rights reserved.

KW - Parity games

KW - Fixed-parameter algorithms

KW - Kernelization

KW - Subexponential algorithms

KW - SUBEXPONENTIAL ALGORITHM

KW - INFINITE GAMES

KW - WIDTH

U2 - 10.1016/j.disopt.2018.06.001

DO - 10.1016/j.disopt.2018.06.001

M3 - Article

SN - 1572-5286

VL - 30

SP - 73

EP - 95

JO - Discrete Optimization

JF - Discrete Optimization

ER -

New deterministic algorithms for solving parity games

Abstract

Keywords

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