Path Puzzles: Discrete Tomography with a Path Constraint is Hard

Jeffrey Bosboom, Erik D. Demaine, Martin L. Demaine, Adam Hesterberg, Roderick Kimball, Justin Kopinsky

We prove that path puzzles with complete row and column information--or equivalently, 2D orthogonal discrete tomography with Hamiltonicity constraint--are strongly NP-complete, ASP-complete, and #P-complete. Along the way, we newly establish ASP-completeness and #P-completeness for 3-Dimensional Matching and Numerical 3-Dimensional Matching.

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