新的盒中蛇记录普查
New Snake-in-the-Box Records via Snakepit Surgery and Learned Construction
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- California Institute of Technology（加州理工学院）
- Universität Zürich（苏黎世大学）
- Imperial College London（伦敦帝国理工学院）
- University of Cambridge（剑桥大学）
机构由 AI 辅助整理，请以论文原文为准。
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中文总结 AI 辅助
研究盒中蛇问题，即求超立方体图\(Q_n\)中最长诱导路径。核心方法是给出\(9\)到\(13\)维度下更长的蛇，主要贡献是提高了\(a(n)\)的下界并提供可验证数据集。
中文摘要 AI 辅助
1958年考茨提出的盒中蛇问题，是求超立方体图\(Q_n\)中最长的诱导（无弦）路径（称为蛇）。已知\(n\leq8\)各维度下的最大长度\(a(n)\)。本文给出了\(9\)到\(13\)各维度中比之前已知最长的蛇更长的蛇，提高了\(a(n)\)的下界，并提供了计算机可验证数据集中所有记录长度的路径。
英文摘要
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.
