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/
Deng, Mingyang ;
Kirkpatrick, Yael ;
Rong, Victor ;
Vassilevska Williams, Virginia ;
Zhong, Ziqian
New Additive Approximations for Shortest Paths and Cycles
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 |