TL;DR
This paper proves that certain path puzzles with complete information are computationally very hard, establishing their NP-completeness and related complexity classifications, and also introduces new complexity results for related problems.
Contribution
It demonstrates the NP-completeness, ASP-completeness, and #P-completeness of path puzzles with complete row and column data, and establishes new complexity results for 3D matching problems.
Findings
Path puzzles are strongly NP-complete, ASP-complete, and #P-complete.
New complexity results for 3-Dimensional Matching and Numerical 3-Dimensional Matching.
Complexity classifications for 2D orthogonal discrete tomography with Hamiltonicity constraint.
Abstract
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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