NP-completeness of generalized Kaboozle
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- Asano Tetsuo
- School of Information Science, Japan Advanced Institute of Science and Technology (JAIST)
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- Demaine Erik D.
- Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology (MIT)
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- Demaine Martin L.
- Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology (MIT)
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- Uehara Ryuhei
- School of Information Science, Japan Advanced Institute of Science and Technology (JAIST)
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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.
Journal
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- Information and Media Technologies
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Information and Media Technologies 7 (3), 1019-1024, 2012
Information and Media Technologies Editorial Board
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Details 詳細情報について
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- CRID
- 1390001205265074432
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- NII Article ID
- 130002116381
- 130002073623
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- NII Book ID
- AA00700121
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- ISSN
- 18810896
- 18826652
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- Text Lang
- en
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- Data Source
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- JaLC
- IRDB
- Crossref
- CiNii Articles
- KAKEN
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- Abstract License Flag
- Disallowed