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.2021.34
URN: urn:nbn:de:0030-drops-141034
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14103/
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Bonnet, Édouard

4 vs 7 Sparse Undirected Unweighted Diameter is SETH-Hard at Time n^{4/3}

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LIPIcs-ICALP-2021-34.pdf (0.8 MB)

Abstract

We show, assuming the Strong Exponential Time Hypothesis, that for every ε > 0, approximating undirected unweighted Diameter on n-vertex m-edge graphs within ratio 7/4 - ε requires m^{4/3 - o(1)} time, even when m = Õ(n). This is the first result that conditionally rules out a near-linear time 5/3-approximation for undirected Diameter.

BibTeX - Entry

@InProceedings{bonnet:LIPIcs.ICALP.2021.34,
  author =	{Bonnet, \'{E}douard},
  title =	{{4 vs 7 Sparse Undirected Unweighted Diameter is SETH-Hard at Time n^\{4/3\}}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14103},
  URN =		{urn:nbn:de:0030-drops-141034},
  doi =		{10.4230/LIPIcs.ICALP.2021.34},
  annote =	{Keywords: Diameter, inapproximability, SETH lower bounds, k-Orthogonal Vectors}
}

Keywords: Diameter, inapproximability, SETH lower bounds, k-Orthogonal Vectors
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021

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