1 × 1 rush hour with fixed blocks is PSPACE-complete
Name
LIPIcs-FUN-2021-7.pdf
Description
Published version
Size
757.13 KB
Format
Adobe PDF
Checksum (MD5)
4fe907e17d2f49969730ea58d6233044
Author(s)
Brunner, Josh
Chung, Lily
Demaine, Erik D
Hendrickson, Dylan H.
Hesterberg, Adam Classen
Zeff, Avi
Date Issued
May 2021
Journal
Leibniz International Proceedings in Informatics, LIPIcs
Publisher
Schloss Dagstuhl, Leibniz Center for Informatics
Citation
Brunner, Josh et al. “1 × 1 rush hour with fixed blocks is PSPACE-complete.” 10th International Conference on Fun with Algorithms, May-June 2021, Favignana Island, Italy, Schloss Dagstuhl and Leibniz Center for Informatics, 2021. © 2021 The Author(s)
Version
Final published version
Abstract
Consider n² - 1 unit-square blocks in an n × n square board, where each block is labeled as movable horizontally (only), movable vertically (only), or immovable - a variation of Rush Hour with only 1 × 1 cars and fixed blocks. We prove that it is PSPACE-complete to decide whether a given block can reach the left edge of the board, by reduction from Nondeterministic Constraint Logic via 2-color oriented Subway Shuffle. By contrast, polynomial-time algorithms are known for deciding whether a given block can be moved by one space, or when each block either is immovable or can move both horizontally and vertically. Our result answers a 15-year-old open problem by Tromp and Cilibrasi, and strengthens previous PSPACE-completeness results for Rush Hour with vertical 1 × 2 and horizontal 2 × 1 movable blocks and 4-color Subway Shuffle.
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 3.0 unported license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.FUN.2021.7
