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Permanent link (DOI): https://doi.org/10.7939/R3XC7P

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Playing and solving the game of Hex Open Access

Descriptions

Other title
Subject/Keyword
algorithms
games
combinatorial game theory
automated solver
Monte Carlo tree search
Hex
proof number search
PSPACE-complete
artificial intelligence
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Henderson, Philip
Supervisor and department
Hayward, Ryan (Computing Science)
Examining committee member and department
Nowakowski, Richard (Mathematics and Statistics, Dalhousie University)
Mueller, Martin (Computing Science)
Shirvani, Mazi (Mathematical and Statistical Sciences)
Culberson, Joseph (Computing Science)
Department
Department of Computing Science
Specialization

Date accepted
2010-08-26T17:38:21Z
Graduation date
2010-11
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
The game of Hex is of interest to the mathematics, algorithms, and artificial intelligence communities. It is a classical PSPACE-complete problem, and its invention is intrinsically tied to the Four Colour Theorem and the well-known strategy-stealing argument. Nash, Shannon, Tarjan, and Berge are among the mathematicians who have researched and published about this game. In this thesis we expand on previous research, further developing the mathematical theory and algorithmic techniques relating to Hex. In particular, we identify new classes of moves that can be pruned from consideration, and devise new algorithms to identify connection strategies efficiently. As a result of these theoretical improvements, we produce an automated solver capable of solving all 8 x 8 Hex openings and most 9 x 9 Hex openings; this marks the first time that computers have solved all Hex openings solved by humans. We also produce the two strongest automated Hex players in the world --- Wolve and MoHex --- and obtain both the gold and silver medals in the 2008 and 2009 International Computer Olympiads.
Language
English
DOI
doi:10.7939/R3XC7P
Rights
License granted by Philip Henderson (ph@cs.ualberta.ca) on 2010-08-25 (GMT): Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of the above terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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