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.2023.85
URN: urn:nbn:de:0030-drops-181377
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18137/
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Kogan, Shimon ; Parter, Merav

New Additive Emulators

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LIPIcs-ICALP-2023-85.pdf (0.8 MB)

Abstract

For a given (possibly weighted) graph G = (V,E), an additive emulator H is a weighted graph in V × V that preserves the (all pairs) G-distances up to a small additive stretch. In their breakthrough result, [Abboud and Bodwin, STOC 2016] ruled out the possibility of obtaining o(n^{4/3})-size emulator with n^{o(1)} additive stretch. The focus of our paper is in the following question that has been explicitly stated in many of the prior work on this topic:
What is the minimal additive stretch attainable with linear size emulators?
The only known upper bound for this problem is given by an implicit construction of [Pettie, ICALP 2007] that provides a linear-size emulator with +Õ(n^{1/4}) stretch. No improvement on this problem has been shown since then.
In this work we improve upon the long standing additive stretch of Õ(n^{1/4}), by presenting constructions of linear-size emulators with Õ(n^{0.222}) additive stretch. Our constructions improve the state-of-the-art size vs. stretch tradeoff in the entire regime. For example, for every ε > 1/7, we provide +n^{f(ε)} emulators of size Õ(n^{1+ε}), for f(ε) = 1/5-3ε/5. This should be compared with the current bound of f(ε) = 1/4-3ε/4 by [Pettie, ICALP 2007].
The new emulators are based on an extended and optimized toolkit for computing weighted additive emulators with sublinear distance error. Our key construction provides a weighted modification of the well-known Thorup and Zwick emulators [SODA 2006]. We believe that this TZ variant might be of independent interest, especially for providing improved stretch for distant pairs.

BibTeX - Entry

@InProceedings{kogan_et_al:LIPIcs.ICALP.2023.85,
  author =	{Kogan, Shimon and Parter, Merav},
  title =	{{New Additive Emulators}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{85:1--85:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18137},
  URN =		{urn:nbn:de:0030-drops-181377},
  doi =		{10.4230/LIPIcs.ICALP.2023.85},
  annote =	{Keywords: Spanners, Emulators, Distance Preservers}
}

Keywords: Spanners, Emulators, Distance Preservers
Collection: 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Issue Date: 2023
Date of publication: 05.07.2023

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