License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2018.43
URN: urn:nbn:de:0030-drops-90475
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9047/
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Duan, Ran ; Lyu, Kaifeng ; Xie, Yuanhang

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

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LIPIcs-ICALP-2018-43.pdf (0.5 MB)

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}.

BibTeX - Entry

@InProceedings{duan_et_al:LIPIcs:2018:9047,
  author =	{Ran Duan and Kaifeng Lyu and Yuanhang Xie},
  title =	{{Single-Source Bottleneck Path Algorithm Faster than Sorting for Sparse Graphs}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{43:1--43:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9047},
  URN =		{urn:nbn:de:0030-drops-90475},
  doi =		{10.4230/LIPIcs.ICALP.2018.43},
  annote =	{Keywords: Graph Algorithm, Bottleneck Path, Combinatorial Optimization}
}

Keywords: Graph Algorithm, Bottleneck Path, Combinatorial Optimization
Collection: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue Date: 2018
Date of publication: 04.07.2018

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