Finding a Hamiltonian Path in a Cube with Specified Turns is Hard
Author(s)Abel, Zachary Ryan; Demaine, Erik D.; Demaine, Martin L.; Eisenstat, Sarah Charmian; Lynch, Jayson R.; Schardl, Tao Benjamin; ... Show more Show less
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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.
DepartmentMassachusetts 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
Journal of Information Processing
Information Processing Society of Japan
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.
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