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: https://drops.dagstuhl.de/opus/volltexte/2021/13662/
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Bonnet, Édouard

Inapproximability of Diameter in Super-Linear Time: Beyond the 5/3 Ratio

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LIPIcs-STACS-2021-17.pdf (0.7 MB)


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


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