Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Bodwin, Greg; Dinitz, Michael; Nazari, Yasamin https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-156217
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Vertex Fault-Tolerant Emulators

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Abstract

A k-spanner of a graph G is a sparse subgraph that preserves its shortest path distances up to a multiplicative stretch factor of k, and a k-emulator is similar but not required to be a subgraph of G. A classic theorem by Althöfer et al. [Disc. Comp. Geom. '93] and Thorup and Zwick [JACM '05] shows that, despite the extra flexibility available to emulators, the size/stretch tradeoffs for spanners and emulators are equivalent. Our main result is that this equivalence in tradeoffs no longer holds in the commonly-studied setting of graphs with vertex failures. That is: we introduce a natural definition of vertex fault-tolerant emulators, and then we show a three-way tradeoff between size, stretch, and fault-tolerance for these emulators that polynomially surpasses the tradeoff known to be optimal for spanners.
We complement our emulator upper bound with a lower bound construction that is essentially tight (within log n factors of the upper bound) when the stretch is 2k-1 and k is either a fixed odd integer or 2. We also show constructions of fault-tolerant emulators with additive error, demonstrating that these also enjoy significantly improved tradeoffs over those available for fault-tolerant additive spanners.

BibTeX - Entry

@InProceedings{bodwin_et_al:LIPIcs.ITCS.2022.25,
  author =	{Bodwin, Greg and Dinitz, Michael and Nazari, Yasamin},
  title =	{{Vertex Fault-Tolerant Emulators}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{25:1--25:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15621},
  URN =		{urn:nbn:de:0030-drops-156217},
  doi =		{10.4230/LIPIcs.ITCS.2022.25},
  annote =	{Keywords: Emulators, Fault Tolerance, Girth Conjecture}
}

Keywords: Emulators, Fault Tolerance, Girth Conjecture
Seminar: 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)
Issue date: 2022
Date of publication: 25.01.2022


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