Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players
Name
2002.03887.pdf
Description
Submitted version
Size
1.32 MB
Format
Adobe PDF
Checksum (MD5)
92b2be14fa7571e02338ea4595ce66c4
Author(s)
Bosboom, Jeffrey
Chen, Charlotte
Chung, Lily
Compton, Spencer
Coulombe, Michael
Demaine, Erik D
Demaine, Martin L
Filho, Ivan Tadeu Ferreira Antunes
Hendrickson, Dylan
Hesterberg, Adam
Date Issued
2020
Journal
Journal of Information Processing
Publisher
Information Processing Society of Japan
Citation
Bosboom, Jeffrey, Chen, Charlotte, Chung, Lily, Compton, Spencer, Coulombe, Michael et al. 2020. "Edge Matching with Inequalities, Triangles, Unknown Shape, and Two Players." Journal of Information Processing, 28 (0).
Version
Original manuscript
Abstract
© 2020 Information Processing Society of Japan. 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-time solvable for nonstrict inequalities. Second we analyze three types of triangular edge matching, of which one is polynomial-time solvable 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 1×n 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., 1 × n edge matching. Along the way, we prove #P-and ASP-completeness of planar 3-regular directed Hamiltonicity; we provide linear-time algorithms to find antidirected and forbidden-transition Eulerian paths; and we characterize the complexity of new partizan variants of the Geography game on graphs.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.2197/IPSJJIP.28.987
