Push-Pull Block Puzzles are Hard
Name
1709.01241.pdf
Description
Accepted version
Size
574.08 KB
Format
Adobe PDF
Checksum (MD5)
3cd17d13a99ba5a035b667e86ed6a925
Author(s)
Demaine, Erik D
Grosof, Isaac B.
Lynch, Jayson R.
Date Issued
April 2017
Journal
CIAC 2017: Algorithms and Complexity
Publisher
Springer International Publishing
Citation
Demaine, Eric D. et al. "Push-Pull Block Puzzles are Hard." CIAC 2017: Algorithms and Complexity, May 2017, Athens, Greece, Springer International Publishing, June 2017 © 2017 Springer International Publishing
Version
Author's final manuscript
Abstract
This paper proves that push-pull block puzzles in 3D are PSPACE-complete to solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve, settling an open question [19]. Push-pull block puzzles are a type of recreational motion planning problem, similar to Sokoban, that involve moving a ‘robot’ on a square grid with 1 × 1 obstacles. The obstacles cannot be traversed by the robot, but some can be pushed and pulled by the robot into adjacent squares. Thin walls prevent movement between two adjacent squares. This work follows in a long line of algorithms and complexity work on similar problems [3– 9, 14, 16, 18]. The 2D push-pull block puzzle shows up in the video games Pukoban as well as The Legend of Zelda: A Link to the Past, giving another proof of hardness for the latter [2]. This variant of block-pushing puzzles is of particular interest because of its connections to reversibility, since any action (e.g., push or pull) can be inverted by another valid action (e.g., pull or push).
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/978-3-319-57586-5_16
