Finding a Hamiltonian Path in a Cube with Specified Turns is Hard
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Demaine_Finding a.pdf
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Author(s)
Abel, Zachary Ryan
Demaine, Erik D.
Demaine, Martin L.
Eisenstat, Sarah Charmian
Lynch, Jayson R.
Schardl, Tao Benjamin
Date Issued
July 2013
Journal
Journal of Information Processing
Publisher
Information Processing Society of Japan
Citation
Abel, Zachary, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, Jayson Lynch, and Tao B. Schardl. “Finding a Hamiltonian Path in a Cube with Specified Turns Is Hard.” Journal of Information Processing 21, no. 3 (2013): 368–377.
Version
Author's final manuscript
Abstract
We prove the NP-completeness of finding a Hamiltonian path in an N × N × N cube graph with turns exactly at specified lengths along the path. This result establishes NP-completeness of Snake Cube puzzles: folding a chain of N3 unit cubes, joined at face centers (usually by a cord passing through all the cubes), into an N × N × N cube. Along the way, we prove a universality result that zig-zag chains (which must turn every unit) can fold into any polycube after 4 × 4 × 4 refinement, or into any Hamiltonian polycube after 2 × 2 × 2 refinement.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.2197/ipsjjip.21.368
