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.ESA.2019.65
URN: urn:nbn:de:0030-drops-111862
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11186/
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Karczmarz, Adam ; Lacki, Jakub

Reliable Hubs for Partially-Dynamic All-Pairs Shortest Paths in Directed Graphs

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LIPIcs-ESA-2019-65.pdf (0.5 MB)

Abstract

We give new partially-dynamic algorithms for the all-pairs shortest paths problem in weighted directed graphs. Most importantly, we give a new deterministic incremental algorithm for the problem that handles updates in O~(mn^(4/3) log{W}/epsilon) total time (where the edge weights are from [1,W]) and explicitly maintains a (1+epsilon)-approximate distance matrix. For a fixed epsilon>0, this is the first deterministic partially dynamic algorithm for all-pairs shortest paths in directed graphs, whose update time is o(n^2) regardless of the number of edges. Furthermore, we also show how to improve the state-of-the-art partially dynamic randomized algorithms for all-pairs shortest paths [Baswana et al. STOC'02, Bernstein STOC'13] from Monte Carlo randomized to Las Vegas randomized without increasing the running time bounds (with respect to the O~(*) notation).
Our results are obtained by giving new algorithms for the problem of dynamically maintaining hubs, that is a set of O~(n/d) vertices which hit a shortest path between each pair of vertices, provided it has hop-length Omega(d). We give new subquadratic deterministic and Las Vegas algorithms for maintenance of hubs under either edge insertions or deletions.

BibTeX - Entry

@InProceedings{karczmarz_et_al:LIPIcs:2019:11186,
  author =	{Adam Karczmarz and Jakub Lacki},
  title =	{{Reliable Hubs for Partially-Dynamic All-Pairs Shortest Paths in Directed Graphs}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{65:1--65:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Michael A. Bender and Ola Svensson and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11186},
  URN =		{urn:nbn:de:0030-drops-111862},
  doi =		{10.4230/LIPIcs.ESA.2019.65},
  annote =	{Keywords: shortest paths, dynamic, incremental, decremental, directed graphs, hubs}
}

Keywords: shortest paths, dynamic, incremental, decremental, directed graphs, hubs
Collection: 27th Annual European Symposium on Algorithms (ESA 2019)
Issue Date: 2019
Date of publication: 06.09.2019

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