New Snake-in-the-Box Records via Snakepit Surgery and Learned Construction
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...
| Authors | Paul Orland, Lucas Fagan, Michele Tarquini et al. |
|---|---|
| Primary category | cs.DM |
| Published | 16 July 2026 |
| Last updated at source | 30 September 2026 |
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