Total Tetris: Tetris with Monominoes, Dominoes, Trominoes, Pentominoes,...
Name
deb6bfad7198314a584a36234557e75812e3.pdf
Description
Accepted version
Size
602.77 KB
Format
Adobe PDF
Checksum (MD5)
d47589fdafa6ace2ad345d7c790769f1
Author(s)
Demaine, Erik D
Demaine, Martin L
Eisenstat, Sarah Charmian
Hesterberg, Adam Classen
Lincoln, Andrea I
Lynch, Jayson R.
Date Issued
2017
Journal
Journal of Information Processing
Publisher
Information Processing Society of Japan
Citation
Demaine, Erik D. et al. "Total Tetris: Tetris with Monominoes, Dominoes, Trominoes, Pentominoes,...." Journal of Information Processing 25 (2017): 515-527 © 2017 Information Processing Society of Japan
Version
Author's final manuscript
Abstract
We consider variations on the classic video game Tetris where pieces are k-ominoes instead of the usual tetrominoes (k = 4), as popularized by the video games ntris and Pentris. We prove that it is NP-complete to survive or clear a given initial board with a given sequence of pieces for each k ≤ 5, complementing the previous NP-completeness result for k = 4. More surprisingly, we show that board clearing is NP-complete for k = 3; and if pieces may not be rotated, then clearing is NP-complete for k = 2 and survival is NP-complete for k = 3. All of these problems can be solved in polynomial time for k = 1.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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.25.515
