Zig-Zag Numberlink is NP-Complete The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Adcock, Aaron, Erik D. Demaine, Martin L. Demaine, Michael P. O’Brien, Felix Reidl, Fernando Sanchez Villaamil, and Blair D. Sullivan. “Zig-Zag Numberlink Is NP-Complete.” Journal of Information Processing 23, no. 3 (2015): 239–245. As Published http://dx.doi.org/10.2197/ipsjjip.23.239 Publisher Information Processing Society of Japan Version Original manuscript Citable link http://hdl.handle.net/1721.1/100008 Terms of Use Creative Commons Attribution-Noncommercial-Share Alike Detailed Terms http://creativecommons.org/licenses/by-nc-sa/4.0/ Zig-Zag Numberlink is NP-Complete Aaron Adcock1, Erik D. Demaine2, Martin L. Demaine2, Michael P. O'Brien3, Felix Reidl4, Fernando S´anchez Villaamil4, and Blair D. Sullivan3 1Stanford University, Palo Alto, CA, USA,
[email protected] 2Massachusetts Institute of Technology, Cambridge, MA, USA, fedemaine,
[email protected] 3North Carolina State University, Raleigh, NC, USA, fmpobrie3,blair
[email protected] 4RWTH Aachen University, Aachen, Germany, freidl,
[email protected] October 23, 2014 Abstract When can t terminal pairs in an m × n grid be connected by t 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.