License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.DISC.2017.44
URN: urn:nbn:de:0030-drops-79874
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7987/
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Bringmann, Karl ; Krinninger, Sebastian

Brief Announcement: A Note on Hardness of Diameter Approximation

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LIPIcs-DISC-2017-44.pdf (0.3 MB)

Abstract

We revisit the hardness of approximating the diameter of a network. In the CONGEST model, ~Omega(n) rounds are necessary to compute the diameter [Frischknecht et al. SODA'12]. Abboud et al. [DISC 2016] extended this result to sparse graphs and, at a more fine-grained level, showed that, for any integer 1 <= l <= polylog(n) , distinguishing between networks of diameter 4l + 2 and 6l + 1 requires ~Omega(n) rounds. We slightly tighten this result by showing that even distinguishing between diameter 2l + 1 and 3l + 1 requires ~Omega(n) rounds. The reduction of Abboud et al. is inspired by recent conditional lower bounds in the RAM model, where the orthogonal vectors problem plays a pivotal role. In our new lower bound, we make the connection to orthogonal vectors explicit, leading to a conceptually more streamlined exposition. This is suited for teaching both the lower bound in the CONGEST model and the conditional lower bound in the RAM model.

BibTeX - Entry

@InProceedings{bringmann_et_al:LIPIcs:2017:7987,
  author =	{Karl Bringmann and Sebastian Krinninger},
  title =	{{Brief Announcement: A Note on Hardness of Diameter Approximation}},
  booktitle =	{31st International Symposium on Distributed Computing (DISC 2017)},
  pages =	{44:1--44:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-053-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{91},
  editor =	{Andr{\'e}a W. Richa},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7987},
  URN =		{urn:nbn:de:0030-drops-79874},
  doi =		{10.4230/LIPIcs.DISC.2017.44},
  annote =	{Keywords: diameter, fine-grained reductions, conditional lower bounds}
}

Keywords: diameter, fine-grained reductions, conditional lower bounds
Collection: 31st International Symposium on Distributed Computing (DISC 2017)
Issue Date: 2017
Date of publication: 12.10.2017

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