三色和双色TANGLE（TM）旋转问题通过简约约化是NP完全的
The Three-Color and Two-Color Tantrix(TM) Rotation Puzzle Problems are NP-Complete via Parsimonious Reductions
摘要：
Holzer和Holzer（Discrete Applied Mathematics 144（3）：345- 358，2004）证明了具有四种颜色的TanjetTM旋转难题是NP完全的，并且他们证明了这个问题的无穷变体是不可判定的。本文研究了三色和双色TanjetTM旋转问题（3-TRP和2-TRP）及其变形。将允许的颜色的数量限制为三种（分别为两种）将可用的TanjetTM瓦片的集合从56减少到14（分别为8）。我们证明了3-TRP和2-TRP是NP-完全的，这肯定地回答了Holzer和Holzer提出的一个问题。由于我们的约简是简约的，因此，在随机约简下，问题Unique-3-TRP和Unique-2-TRP是DP-完全的。我们还证明了与4-TRP，3-TRP和2-TRP相关的另一解问题是NP-完全的。最后证明了3-TRP和2-TRP的无穷变体是不可判定的。
英文摘要：
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.
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