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arXiv · 1808.10658

Single-Source Bottleneck Path Algorithm Faster than Sorting for Sparse Graphs

Ran Duan·Kaifeng Lyu·Hongxun Wu·Yuanhang Xie
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Abstract

In a directed graph $G=(V,E)$ with a capacity on every edge, a \emph{bottleneck path} (or \emph{widest path}) between two vertices is a path maximizing the minimum capacity of edges in the path. For the single-source all-destination version of this problem in directed graphs, the previous best algorithm runs in $O(m+n\log n)$ ($m=|E|$ and $n=|V|$) time, by Dijkstra search with Fibonacci heap [Fredman and Tarjan 1987]. We improve this time bound to $O(m\sqrt{\log n})$, thus it is the first algorithm which breaks the time bound of classic Fibonacci heap when $m=o(n\sqrt{\log n})$. It is a Las-Vegas randomized approach. By contrast, the s-t bottleneck path has an algorithm with running time $O(m\beta(m,n))$ [Chechik et al. 2016], where $\beta(m,n)=\min\{k\geq 1: \log^{(k)}n\leq\frac{m}{n}\}$.

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Ran Duan, Kaifeng Lyu, Hongxun Wu, Yuanhang Xie. 2018-08-31. Single-Source Bottleneck Path Algorithm Faster than Sorting for Sparse Graphs. https://arxiv.org/abs/1808.10658

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