发表机构
CWI, Amsterdam, The Netherlands; Vrije Universiteit Amsterdam, The Netherlands; TTIC, Chicago, United States（荷兰阿姆斯特丹CWI; 荷兰阿姆斯特丹自由大学; 美国芝加哥陶尔森理论计算机科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对有向跳集、捷径集和距离保持器三类结构，提出匹配最优权衡的更快算法，其中跳集算法先针对DAG设计再扩展至一般图，捷径集为确定性算法，距离保持器算法基于跳集结构加速归约。
AI 中文摘要
尽管近期在优化有向距离结构（如跳集、捷径集和距离保持器）的权衡方面取得了诸多进展，但多数已知算法效率低下。本研究取得三项成果：一是针对有向(1+ε)-跳集的更快算法，匹配Bernstein与Wein[SODA23]的最优规模/跳界权衡，算法先针对有向无环图（DAG）设计，再利用Haeupler、Jiang与Saranurak[STOC26]的最新DAG投影结果扩展至一般图（仅存在n^{o(1)}级因子）；二是构造捷径集的更快确定性算法，匹配Kogan与Parter[SODA22A]的最优规模/跳界权衡；三是利用改进的有向跳集构造，得到计算源端距离保持器的显著更快算法，该算法基于Kogan与Parter[SODA22B]的归约加速，通过利用所构造跳集的特定结构性质实现。
英文摘要
While there have been many recent advances in getting better tradeoffs for directed distance structures such as hopsets, shortcut sets and distance preservers, most known algorithms are inefficient. In this work we provide three results: - Faster algorithms for directed $(1+ε)$-hopsets, matching the state-of-the-art size/hopbound trade-offs of Bernstein & Wein [SODA23]. Our algorithm is first designed for DAGs and then extended to general graphs (up to $n^{o(1)}$ factors) using the recent DAG projection result of Haeupler, Jiang, and Saranurak [STOC26]. - Faster \textit{deterministic} algorithms for constructing shortcut sets, matching the state-of-the-art size/hopbound tradeoffs of Kogan & Parter [SODA22A]. - Using our improved directed hopset construction, we get significantly faster algorithms for computing source-wise distance preservers. This algorithm is based on speeding-up reductions of Kogan & Parter [SODA22B] by using certain structural properties of our hopsets.
