License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2022.50
URN: urn:nbn:de:0030-drops-163919
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16391/
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Deng, Mingyang ; Kirkpatrick, Yael ; Rong, Victor ; Vassilevska Williams, Virginia ; Zhong, Ziqian

New Additive Approximations for Shortest Paths and Cycles

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LIPIcs-ICALP-2022-50.pdf (0.7 MB)

Abstract

This paper considers additive approximation algorithms for All-Pairs Shortest Paths (APSP) and Shortest Cycle in undirected unweighted graphs. The results are as follows:
- We obtain the first +2-approximation algorithm for APSP in n-vertex graphs that improves upon Dor, Halperin and Zwick’s (SICOMP'00) Õ(n^{7/3}) time algorithm. The new algorithm runs in Õ(n^2.29) time and is obtained via a reduction to Min-Plus product of bounded difference matrices.
- We obtain the first additive approximation scheme for Shortest Cycle, generalizing the approximation algorithms of Itai and Rodeh (SICOMP'78) and Roditty and Vassilevska W. (SODA'12). For every integer r ≥ 0, we give an Õ(n+n^{2+r}/m^r) time algorithm that returns a +(2r+1)-approximate shortest cycle in any n-vertex, m-edge graph.

BibTeX - Entry

@InProceedings{deng_et_al:LIPIcs.ICALP.2022.50,
  author =	{Deng, Mingyang and Kirkpatrick, Yael and Rong, Victor and Vassilevska Williams, Virginia and Zhong, Ziqian},
  title =	{{New Additive Approximations for Shortest Paths and Cycles}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{50:1--50:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16391},
  URN =		{urn:nbn:de:0030-drops-163919},
  doi =		{10.4230/LIPIcs.ICALP.2022.50},
  annote =	{Keywords: Fine-grained Complexity, Additive Approximation}
}

Keywords: Fine-grained Complexity, Additive Approximation
Collection: 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)
Issue Date: 2022
Date of publication: 28.06.2022

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