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an integer programming approach to solving tantrix on fixed boards整数规划的方法来解决tantrix固定板
Algorithms 2012, 5, 158-175; doi:10.3390/a5010158
OPEN ACCESS
algorithms
ISSN 1999-4893
/journal/algorithms
Article
An Integer Programming Approach to Solving Tantrix on
Fixed Boards
Fumika Kino 1 and Yushi Uno 2,*
1 Mitsubishi Electric Information Network Corp., 8-1-1 Tsukaguchi-Honmachi, Amagasaki 661-8611,
Japan; E-Mail: tanukinoko0049@
2 Graduate School of Science, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai
599-8531, Japan
⋆ Author to whom correspondence should be addressed; E-Mail: uno@mi.s.osakafu-u.ac.jp;
Tel.: +81-72-254-9930.
Received: 15 December 2011; in revised form: 9 March 2012 / Accepted: 14 March 2012 /
Published: 22 March 2012
R
Abstract: Tantrix (Tantrix⃝ is a registered trademark of Colour of Strategy Ltd. in
New Zealand, and of TANTRIX JAPAN in Japan, respectively, under the license of
M. McManaway, the inventor.) is a puzzle to make a loop by connecting lines drawn on
hexagonal tiles, and the objective of this research is to solve it by a computer. For this
purpose, we first give a problem setting of solving Tantrix as making a loop on a given fixed
board. We then formulate it as an integer program by describing the rules of Tantrix as its
constraints, and solve it by a mathematical programming solver to have a solution. As a
result, we establish a formulation that can solve Tantrix of moderate size, and even when the
solutions are invalid only by elementary constraints, we achiev
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