改进的有向单源最短路径的强多项式工作-跨度权衡
Improved Strongly Polynomial Work-Span Tradeoffs for Directed Single Source Shortest Paths
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中文总结 AI 辅助
研究有向图单源最短路径问题，给出确定性并行算法，其工作为\(O(n^{1 + o(1)}t^2 + m^{1 + o(1)})\)，跨度为\(\tilde{O}(n/t)\)，在亚多项式因子上匹配无向图相关权衡。
中文摘要 AI 辅助
我们重新审视了具有非负实权重的有向图上的单源最短路径（SSSP）问题，并给出了一种确定性并行算法。该算法对于任意\(t\in[1,n]\)，工作为\(O(n^{1 + o(1)}t^2 + m^{1 + o(1)})\)，跨度为\(\tilde{O}(n/t)\)。这在亚多项式因子范围内与[Shi和Spencer '99]针对具有非负实权重的无向图的权衡相匹配。
英文摘要
We revisit the single-source shortest paths (SSSP) problem on directed graphs with nonnegative real weights and give a deterministic parallel algorithm with $O(n^{1+o(1)}t^2 + m^{1+o(1)})$ work and $\tilde{O}(n/t)$ span, for any $t \in [1, n]$. This matches (up to subpolynomial factors) the tradeoff due to [Shi and Spencer '99] for undirected graphs with nonnegative real weights.
