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DOI: 10.4230/LIPIcs.FUN.2021.7
URN: urn:nbn:de:0030-drops-127681
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12768/
Brunner, Josh ; Chung, Lily ; Demaine, Erik D. ; Hendrickson, Dylan ; Hesterberg, Adam ; Suhl, Adam ; Zeff, Avi
1 X 1 Rush Hour with Fixed Blocks Is PSPACE-Complete
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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.
BibTeX - Entry
@InProceedings{brunner_et_al:LIPIcs:2020:12768,
author = {Josh Brunner and Lily Chung and Erik D. Demaine and Dylan Hendrickson and Adam Hesterberg and Adam Suhl and Avi Zeff},
title = {{1 X 1 Rush Hour with Fixed Blocks Is PSPACE-Complete}},
booktitle = {10th International Conference on Fun with Algorithms (FUN 2021)},
pages = {7:1--7:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-145-0},
ISSN = {1868-8969},
year = {2020},
volume = {157},
editor = {Martin Farach-Colton and Giuseppe Prencipe and Ryuhei Uehara},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12768},
URN = {urn:nbn:de:0030-drops-127681},
doi = {10.4230/LIPIcs.FUN.2021.7},
annote = {Keywords: puzzles, sliding blocks, PSPACE-hardness}
}
| Keywords: | puzzles, sliding blocks, PSPACE-hardness | |
| Seminar: | 10th International Conference on Fun with Algorithms (FUN 2021) | |
| Issue date: | 2020 | |
| Date of publication: | 16.09.2020 |
