1 research outputs found
The Three-Color and Two-Color Tantrix(TM) Rotation Puzzle Problems are NP-Complete via Parsimonious Reductions
Holzer and Holzer (Discrete Applied Mathematics 144(3):345--358, 2004) proved
that the Tantrix(TM) rotation puzzle problem with four colors is NP-complete,
and they showed that the infinite variant of this problem is undecidable. In
this paper, we study the three-color and two-color Tantrix(TM) rotation puzzle
problems (3-TRP and 2-TRP) and their variants. Restricting the number of
allowed colors to three (respectively, to two) reduces the set of available
Tantrix(TM) tiles from 56 to 14 (respectively, to 8). We prove that 3-TRP and
2-TRP are NP-complete, which answers a question raised by Holzer and Holzer in
the affirmative. Since our reductions are parsimonious, it follows that the
problems Unique-3-TRP and Unique-2-TRP are DP-complete under randomized
reductions. We also show that the another-solution problems associated with
4-TRP, 3-TRP, and 2-TRP are NP-complete. Finally, we prove that the infinite
variants of 3-TRP and 2-TRP are undecidable.Comment: 30 pages, 25 figure