Journal of Information Processing
Online ISSN : 1882-6652
ISSN-L : 1882-6652
Finding a Hamiltonian Path in a Cube with Specified Turns is Hard
Zachary AbelErik D. DemaineMartin L. DemaineSarah EisenstatJayson LynchTao B. Schardl
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2013 Volume 21 Issue 3 Pages 368-377


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.

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© 2013 by the Information Processing Society of Japan
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