Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players
Abstract
We analyze the computational complexity of several new variants of edge-matching puzzles. First we analyze inequality (instead of equality) constraints between adjacent tiles, proving the problem NP-complete for strict inequalities but polynomial for nonstrict inequalities. Second we analyze three types of triangular edge matching, of which one is polynomial and the other two are NP-complete; all three are #P-complete. Third we analyze the case where no target shape is specified, and we merely want to place the (square) tiles so that edges match (exactly); this problem is NP-complete. Fourth we consider four 2-player games based on edge matching, all four of which are PSPACE-complete. Most of our NP-hardness reductions are parsimonious, newly proving #P and ASP-completeness for, e.g., edge matching.
Cite
@article{arxiv.2002.03887,
title = {Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players},
author = {Jeffrey Bosboom and Charlotte Chen and Lily Chung and Spencer Compton and Michael Coulombe and Erik D. Demaine and Martin L. Demaine and Ivan Tadeu Ferreira Antunes Filho and Dylan Hendrickson and Adam Hesterberg and Calvin Hsu and William Hu and Oliver Korten and Zhezheng Luo and Lillian Zhang},
journal= {arXiv preprint arXiv:2002.03887},
year = {2020}
}
Comments
29 pages, 18 figures. Thorough revisions of Sections 4, 5, and 6/7 (merged)