arXiv subjects
Publications and source records attributed to Papangkorn Apinyanon.
We prove that the solution-search problem for the pencil puzzle Ice Walk is ASP-complete. Our reduction maps Hamiltonian cycles in an undirected maximum-degree-3 spanning subgraph of a rectangular grid graph bijectively to Ice Walk solutions.
All or Nothing, Water Walk, and Remembered Length are pencil puzzles that involve constructing a continuous loop on a rectangular grid under specific constraints. In this paper, we analyze their computational complexity using the T-metacell framework developed by Tang and MIT Hardness Group. We establish that the puzzles are NP-complete by providing reductions; the first two puzzles, from the problem of finding a Hamiltonian cycle in a maximum-degree-3 spanning subgraph of a rectangular grid graph, and the last, from the problem of finding a Hamiltonian cycle in a required-edge directed rectangular grid graph.