An Integer Programming Approach to Solving Tantrix on Fixed Boards
AbstractTantrix (Tantrix R ⃝ 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 achieved it by introducing additional constraints and re-solve it. By this approach we succeeded to solve Tantrix of size up to 60.
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Kino, F.; Uno, Y. An Integer Programming Approach to Solving Tantrix on Fixed Boards. Algorithms 2012, 5, 158-175.
Kino F, Uno Y. An Integer Programming Approach to Solving Tantrix on Fixed Boards. Algorithms. 2012; 5(1):158-175.Chicago/Turabian Style
Kino, Fumika; Uno, Yushi. 2012. "An Integer Programming Approach to Solving Tantrix on Fixed Boards." Algorithms 5, no. 1: 158-175.