Kaboozle Is NP-complete, even in a Strip
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Demaine_Kaboozle is.pdf
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148.64 KB
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Adobe PDF
Checksum (MD5)
0af978c10e44dcd5d3eb2fc5a58d0ac3
Author(s)
Asano, Tetsuo
Demaine, Erik D.
Demaine, Martin L.
Uehara, Ryuhei
Date Issued
January 2010
Journal
Fun with algorithms (International Conference) / Lecture notes in computer science
Publisher
Springer
Citation
Tetsuo, Asano, et al. "Kaboozle is NP-complete, even in a strip" Fun with algorithms, 2010. (Lecture notes in computer science ; v. 6099)28-36. Copyright © 2010, Springer
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/978-3-642-13122-6_5
