Lazy search trees (Sandlund & Wild FOCS 2020, Sandlund & Zhang SODA 2022) are sorted dictionaries whose update and query performance smoothly interpolates between that of efficient priority queues and binary search trees - automatically, depending on actual use; no adjustments are necessary to the data structure to realize the cost savings. In this paper, we design lazy B-trees, a variant of lazy search trees suitable for external memory that generalizes the speedup of B-trees over binary search trees wrt. input/output operations to the same smooth interpolation regime. A key technical difficulty to overcome is the lack of a (fully satisfactory) external variant of biased search trees, on which lazy search trees crucially rely. We give a construction for a subset of performance guarantees sufficient to realize external-memory lazy search trees, which we deem of independent interest.

翻译：惰性搜索树（Sandlund & Wild FOCS 2020, Sandlund & Zhang SODA 2022）是一种排序字典，其更新和查询性能可在高效优先队列与二叉搜索树之间平滑插值——这种插值根据实际使用情况自动实现，无需对数据结构进行调整即可实现成本节约。本文设计了惰性B树，这是一种适用于外部存储的惰性搜索树变体，它将B树相对于二叉搜索树在输入/输出操作上的加速优势推广至相同的平滑插值机制。需要克服的关键技术难点在于缺乏（完全令人满意的）偏置搜索树的外部存储变体，而惰性搜索树的核心依赖于此类结构。我们针对实现外部存储惰性搜索树所需的部分性能保证提出了构建方法，这一成果本身具有独立的研究价值。