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

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Ran Duan, Kaifeng Lyu, and Yuanhang Xie. Single-Source Bottleneck Path Algorithm Faster than Sorting for Sparse Graphs. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 43:1-43:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.ICALP.2018.43

Abstract

In a directed graph G=(V,E) with a capacity on every edge, a bottleneck path (or 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}+sqrt{mn log n log log n}), which is O(n sqrt{log n log log n}) when m=O(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 algorithm with running time O(m beta(m,n)) [Chechik et al. 2016], where beta(m,n)=min{k >= 1: log^{(k)}n <= m/n}.

Subject Classification

ACM Subject Classification
• Theory of computation → Design and analysis of algorithms
Keywords
• Graph Algorithm
• Bottleneck Path
• Combinatorial Optimization

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