PreprintCC BY 4.0arXiv
New Snake-in-the-Box Records via Snakepit Surgery and Learned Construction
Abstract
The snake-in-the-box problem asks for a longest induced path in the hypercube graph Qn. We find a length-191 snake in dimension n=9, the lowest dimension where the maximum is unknown, improving the previous record of 190 that had stood for 14 years. We also establish new lower bounds in dimensions 10-13. To find these records, we introduce snakepits, collections of disjoint snakes, to expand the search space and open new routes between snakes. This motivates our new Snakepit-in-the-Box benchmark, which seeks maximal edge counts when allowing multiple components. Finally, we introduce Beam Anchor, a search-supervised learned constructor algorithm that finds 100 inequivalent length-190 snakes in dimension 9.
Related
BibTeX
@misc{orland2026snakeinthebox,
title = {{New Snake-in-the-Box Records via Snakepit Surgery and Learned Construction}},
author = {Paul Orland and Lucas Fagan and Michele Tarquini and Davide Passaro and Maksymilian Manko and Elli Heyes and Angus Gruen and Giorgi Butbaia and Justin Tan and Sergei Gukov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.15270},
eprint = {2607.15270},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.15270},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - New Snake-in-the-Box Records via Snakepit Surgery and Learned Construction
AU - Paul Orland
AU - Lucas Fagan
AU - Michele Tarquini
AU - Davide Passaro
AU - Maksymilian Manko
AU - Elli Heyes
AU - Angus Gruen
AU - Giorgi Butbaia
AU - Justin Tan
AU - Sergei Gukov
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2607.15270
UR - https://arxiv.org/abs/2607.15270
AB - The snake-in-the-box problem asks for a longest induced path in the hypercube graph Q_n. We find a length-191 snake in dimension n=9, the lowest dimension where the maximum is unknown, improving the previous record of 190 that had stood for 14 years. We also establish new lower bounds in dimensions 10-13. To find these records, we introduce snakepits, collections of disjoint snakes, to expand the search space and open new routes between snakes. This motivates our new Snakepit-in-the-Box benchmark, which seeks maximal edge counts when allowing multiple components. Finally, we introduce Beam Anchor, a search-supervised learned constructor algorithm that finds 100 inequivalent length-190 snakes in dimension 9.
ER -