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.DISC.2022.32
URN: urn:nbn:de:0030-drops-172239
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17223/
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Parter, Merav ; Petruschka, Asaf

Õptimal Dual Vertex Failure Connectivity Labels

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LIPIcs-DISC-2022-32.pdf (1 MB)

Abstract

In this paper we present succinct labeling schemes for supporting connectivity queries under vertex faults. For a given n-vertex graph G, an f-VFT (resp., EFT) connectivity labeling scheme is a distributed data structure that assigns each of the graph edges and vertices a short label, such that given the labels of a vertex pair u and v, and the labels of at most f failing vertices (resp., edges) F, one can determine if u and v are connected in G ⧵ F. The primary complexity measure is the length of the individual labels. Since their introduction by [Courcelle, Twigg, STACS '07], FT labeling schemes have been devised only for a limited collection of graph families. A recent work [Dory and Parter, PODC 2021] provided EFT labeling schemes for general graphs under edge failures, leaving the vertex failure case fairly open.
We provide the first sublinear f-VFT labeling schemes for f ≥ 2 for any n-vertex graph. Our key result is 2-VFT connectivity labels with O(log³ n) bits. Our constructions are based on analyzing the structure of dual failure replacement paths on top of the well-known heavy-light tree decomposition technique of [Sleator and Tarjan, STOC 1981]. We also provide f-VFT labels with sub-linear length (in |V|) for any f = o(log log n), that are based on a reduction to the existing EFT labels.

BibTeX - Entry

@InProceedings{parter_et_al:LIPIcs.DISC.2022.32,
  author =	{Parter, Merav and Petruschka, Asaf},
  title =	{{\~{O}ptimal Dual Vertex Failure Connectivity Labels}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{32:1--32:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17223},
  URN =		{urn:nbn:de:0030-drops-172239},
  doi =		{10.4230/LIPIcs.DISC.2022.32},
  annote =	{Keywords: Fault-Tolerance, Heavy-Light Decomposition, Labeling Schemes}
}

Keywords: Fault-Tolerance, Heavy-Light Decomposition, Labeling Schemes
Collection: 36th International Symposium on Distributed Computing (DISC 2022)
Issue Date: 2022
Date of publication: 17.10.2022

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