eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-07-04
43:1
43:14
10.4230/LIPIcs.ICALP.2018.43
article
Single-Source Bottleneck Path Algorithm Faster than Sorting for Sparse Graphs
Duan, Ran
1
Lyu, Kaifeng
1
Xie, Yuanhang
1
Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China
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}.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol107-icalp2018/LIPIcs.ICALP.2018.43/LIPIcs.ICALP.2018.43.pdf
Graph Algorithm
Bottleneck Path
Combinatorial Optimization