Paper by Erik D. Demaine
- Tetsuo Asano, Erik D. Demaine, Martin L. Demaine, and Ryuhei Uehara, “NP-completeness of generalized Kaboozle”, Journal of Information Processing, volume 20, number 3, July 2012, pages 713–718.
Kaboozle is a puzzle consisting of several square cards, each annotated with
colored paths and dots drawn on both sides and holes drilled. The goal is to
join two colored dots with paths of the same color (and fill all holes) by
stacking the cards suitably. The freedoms here are to reflect, rotate, and
order the cards arbitrarily, so it is not surprising that the problem is
NP-complete (as we show). More surprising is that any one of these
freedoms—reflection, rotation, and order—is alone enough to make the
puzzle NP-complete. Furthermore, we show NP-completeness of a particularly
constrained form of Kaboozle related to 1D paper folding. Specifically, we
suppose that the cards are glued together into a strip, where each glued edge
has a specified folding direction (mountain or valley). This variation removes
the ability to rotate and reflect cards, and restricts the order to be a valid
folded state of a given 1D mountain-valley pattern.
- This paper is also available from J-STAGE.
- The paper is available in PDF (627k).
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- Related papers:
- Kaboozle_FUN2010 (Kaboozle is NP-complete, even in a Strip)
See also other papers by Erik Demaine.
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