Zig-Zag Numberlink is NP-Complete
Computational Complexity
2014-10-23 v1
Abstract
When can terminal pairs in an grid be connected by vertex-disjoint paths that cover all vertices of the grid? We prove that this problem is NP-complete. Our hardness result can be compared to two previous NP-hardness proofs: Lynch's 1975 proof without the ``cover all vertices'' constraint, and Kotsuma and Takenaga's 2010 proof when the paths are restricted to have the fewest possible corners within their homotopy class. The latter restriction is a common form of the famous Nikoli puzzle \emph{Numberlink}; our problem is another common form of Numberlink, sometimes called \emph{Zig-Zag Numberlink} and popularized by the smartphone app \emph{Flow Free}.
Cite
@article{arxiv.1410.5845,
title = {Zig-Zag Numberlink is NP-Complete},
author = {Aaron Adcock and Erik D. Demaine and Martin L. Demaine and Michael P. O'Brien and Felix Reidl and Fernando Sánchez Villaamil and Blair D. Sullivan},
journal= {arXiv preprint arXiv:1410.5845},
year = {2014}
}