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Zig-Zag Numberlink is NP-Complete

Aaron Adcock, Erik D. Demaine, Martin L. Demaine, Michael P. O'Brien, Felix Reidl, Fernando Sánchez Villaamil, Blair D. Sullivan
2015 Journal of Information Processing  
We prove that this problem is NP-complete.  ...  Our problem is another common form of Numberlink, sometimes called Zig-Zag Numberlink and popularized by the smartphone app Flow Free.  ...  The authors were introduced to Zig-Zag Numberlink through Philip Klein (one of the participants), who in turn was introduced through his daughter Simone Klein.  ... 
doi:10.2197/ipsjjip.23.239 fatcat:6x624q4junc57aesma4c2ujm5a

Zig-Zag Numberlink is NP-Complete [article]

Aaron Adcock, Erik D. Demaine, Martin L. Demaine, Michael P. O'Brien, Felix Reidl, Fernando Sánchez Villaamil, Blair D. Sullivan
2014 arXiv   pre-print
We prove that this problem is NP-complete.  ...  The latter restriction is a common form of the famous Nikoli puzzle Numberlink; our problem is another common form of Numberlink, sometimes called Zig-Zag Numberlink and popularized by the smartphone app  ...  The authors were introduced to Zig-Zag Numberlink through Philip Klein (one of the participants), who in turn was introduced through his daughter Simone Klein.  ... 
arXiv:1410.5845v1 fatcat:kyuckuqrw5cb5nqr54fyjrvaqu

Physical Zero-knowledge Proofs for Flow Free, Hamiltonian Cycles, and Many-to-many k-disjoint Covering Paths [article]

Eammon Hart, Joshua A. McGinnis
2022 arXiv   pre-print
Past study of the game has primarily been from the computer science direction, with solving Flow Free and Zig Zag Numberlink being shown to be NP Complete [1] , algorithmic explorations enumerating all  ...  It should also be noted that this paper sits in a young, but growing literature of perfectly sound physical zero-knowledge proofs that also includes Zig-zag Numberlink [19] , Ripple Effect [20] , Sudoku  ... 
arXiv:2202.04113v1 fatcat:jgc4mzneu5eilio6i3izuzsucq

On the Complexity of Two Dots for Narrow Boards and Few Colors

Davide Bilò, Luciano Gualà, Stefano Leucci, Neeldhara Misra, Marc Herbstritt
2018 Fun with Algorithms  
The computational complexity of Two Dots has already been addressed in [Misra, FUN 2016], where it has been shown that the general version of the problem is NP-complete.  ...  The goal is to remove a certain number of dots of each color using a limited number of moves.  ...  This problem is also known as Zig-Zag Numberlink and has been shown to be NP-complete in [1] .  ... 
doi:10.4230/lipics.fun.2018.7 dblp:conf/fun/BiloG0M18 fatcat:gkiclr4hsfdethxiiwhmt46pty