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.STACS.2021.17
URN: urn:nbn:de:0030-drops-136623
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13662/
Bonnet, Édouard
Inapproximability of Diameter in Super-Linear Time: Beyond the 5/3 Ratio
Abstract
We show, assuming the Strong Exponential Time Hypothesis, that for every ε > 0, approximating directed Diameter on m-arc graphs within ratio 7/4 - ε requires m^{4/3 - o(1)} time. Our construction uses non-negative edge weights but even holds for sparse digraphs, i.e., for which the number of vertices n and the number of arcs m satisfy m = O˜(n). This is the first result that conditionally rules out a near-linear time 5/3-approximation for a variant of Diameter.
BibTeX - Entry
@InProceedings{bonnet:LIPIcs.STACS.2021.17,
author = {Bonnet, \'{E}douard},
title = {{Inapproximability of Diameter in Super-Linear Time: Beyond the 5/3 Ratio}},
booktitle = {38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
pages = {17:1--17:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-180-1},
ISSN = {1868-8969},
year = {2021},
volume = {187},
editor = {Bl\"{a}ser, Markus and Monmege, Benjamin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/13662},
URN = {urn:nbn:de:0030-drops-136623},
doi = {10.4230/LIPIcs.STACS.2021.17},
annote = {Keywords: Diameter, inapproximability, SETH lower bounds, k-Orthogonal Vectors}
}
|
Keywords: |
|
Diameter, inapproximability, SETH lower bounds, k-Orthogonal Vectors |
|
Collection: |
|
38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021) |
|
Issue Date: |
|
2021 |
|
Date of publication: |
|
10.03.2021 |
