Deterministic Graphical Games Revisited

Klas Olof Daniel Andersson; Kristoffer Arnsfelt Hansen; Peter Bro Miltersen; Troels Bjerre Sørensen

doi:10.1093/logcom/exq001

Deterministic Graphical Games Revisited

Klas Olof Daniel Andersson, Kristoffer Arnsfelt Hansen, Peter Bro Miltersen, Troels Bjerre Sørensen

Institut for Datalogi

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Abstract

Starting from Zermelo’s classical formal treatment of chess, we trace through history the analysis of two-player win/lose/draw games with perfect information and potentially infinite play. Such chess-like games have appeared in many different research communities, and methods for solving them, such as retrograde analysis, have been rediscovered independently. We then revisit Washburn’s deterministic graphical games (DGGs), a natural generalization of chess-like games to arbitrary zero-sum payoffs. We study the complexity of solving DGGs and obtain an almost-linear time comparison-based algorithm for finding optimal strategies in such games. The existence of a linear time comparison-based algorithm remains an open problem.

Originalsprog	Engelsk
Tidsskrift	Journal of Logic and Computation
Vol/bind	22
Nummer	2
Sider (fra-til)	165-178
Antal sider	14
ISSN	0955-792X
DOI	https://doi.org/10.1093/logcom/exq001
Status	Udgivet - 2012

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10.1093/logcom/exq001

http://logcom.oxfordjournals.org/content/22/2/165.abstract

Citationsformater

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title = "Deterministic Graphical Games Revisited",

abstract = "Starting from Zermelo{\textquoteright}s classical formal treatment of chess, we trace through history the analysis of two-player win/lose/draw games with perfect information and potentially infinite play. Such chess-like games have appeared in many different research communities, and methods for solving them, such as retrograde analysis, have been rediscovered independently. We then revisit Washburn{\textquoteright}s deterministic graphical games (DGGs), a natural generalization of chess-like games to arbitrary zero-sum payoffs. We study the complexity of solving DGGs and obtain an almost-linear time comparison-based algorithm for finding optimal strategies in such games. The existence of a linear time comparison-based algorithm remains an open problem. ",

author = "Andersson, {Klas Olof Daniel} and Hansen, {Kristoffer Arnsfelt} and Miltersen, {Peter Bro} and S{\o}rensen, {Troels Bjerre}",

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doi = "10.1093/logcom/exq001",

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T1 - Deterministic Graphical Games Revisited

AU - Andersson, Klas Olof Daniel

AU - Hansen, Kristoffer Arnsfelt

AU - Miltersen, Peter Bro

AU - Sørensen, Troels Bjerre

PY - 2012

Y1 - 2012

N2 - Starting from Zermelo’s classical formal treatment of chess, we trace through history the analysis of two-player win/lose/draw games with perfect information and potentially infinite play. Such chess-like games have appeared in many different research communities, and methods for solving them, such as retrograde analysis, have been rediscovered independently. We then revisit Washburn’s deterministic graphical games (DGGs), a natural generalization of chess-like games to arbitrary zero-sum payoffs. We study the complexity of solving DGGs and obtain an almost-linear time comparison-based algorithm for finding optimal strategies in such games. The existence of a linear time comparison-based algorithm remains an open problem.

AB - Starting from Zermelo’s classical formal treatment of chess, we trace through history the analysis of two-player win/lose/draw games with perfect information and potentially infinite play. Such chess-like games have appeared in many different research communities, and methods for solving them, such as retrograde analysis, have been rediscovered independently. We then revisit Washburn’s deterministic graphical games (DGGs), a natural generalization of chess-like games to arbitrary zero-sum payoffs. We study the complexity of solving DGGs and obtain an almost-linear time comparison-based algorithm for finding optimal strategies in such games. The existence of a linear time comparison-based algorithm remains an open problem.

U2 - 10.1093/logcom/exq001

DO - 10.1093/logcom/exq001

M3 - Journal article

SN - 0955-792X

VL - 22

SP - 165

EP - 178

JO - Journal of Logic and Computation

JF - Journal of Logic and Computation

IS - 2

ER -

Deterministic Graphical Games Revisited

Abstract

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