稀疏图谱中的全动态最短路径

arXiv - CS - Data Structures and Algorithms Pub Date : 2024-08-26 DOI:arxiv-2408.14406

Adam Karczmarz, Piotr Sankowski

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引用次数: 0

摘要

我们研究了精确的全动态最短路径问题。对于实加权有向图，我们展示了一种确定性全动态数据结构，其最坏情况下的更新时间为$\tilde{O}(mn^{4/5})$，处理任意$s,t$距离查询的时间为$\tilde{O}(n^{4/5})$。这是在稀疏加权有向图体系中，该问题的首次非难更新/查询权衡。

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Fully Dynamic Shortest Paths in Sparse Digraphs

We study the exact fully dynamic shortest paths problem. For real-weighted directed graphs, we show a deterministic fully dynamic data structure with $\tilde{O}(mn^{4/5})$ worst-case update time processing arbitrary $s,t$-distance queries in $\tilde{O}(n^{4/5})$ time. This constitutes the first non-trivial update/query tradeoff for this problem in the regime of sparse weighted directed graphs.

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arXiv - CS - Data Structures and Algorithms

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