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.OPODIS.2022.22
URN: urn:nbn:de:0030-drops-176420
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17642/
Go to the corresponding LIPIcs Volume Portal

Liu, Shihao

The Impossibility of Approximate Agreement on a Larger Class of Graphs

pdf-format:
LIPIcs-OPODIS-2022-22.pdf (0.7 MB)

Abstract

Approximate agreement is a variant of consensus in which processes receive input values from a domain and must output values in that domain that are sufficiently close to one another. We study the problem when the input domain is the vertex set of a connected graph. In asynchronous systems where processes communicate using shared registers, there are wait-free approximate agreement algorithms when the graph is a path or a tree, but not when the graph is a cycle of length at least 4. For many graphs, it is unknown whether a wait-free solution for approximate agreement exists.
We introduce a set of impossibility conditions and prove that approximate agreement on graphs satisfying these conditions cannot be solved in a wait-free manner. In particular, the graphs of all triangulated d-dimensional spheres that are not cliques, satisfy these conditions. The vertices and edges of an octahedron is an example of such a graph. We also present a family of reductions from approximate agreement on one graph to another graph. This allows us to extend known impossibility results to even more graphs.

BibTeX - Entry

@InProceedings{liu:LIPIcs.OPODIS.2022.22,
  author =	{Liu, Shihao},
  title =	{{The Impossibility of Approximate Agreement on a Larger Class of Graphs}},
  booktitle =	{26th International Conference on Principles of Distributed Systems (OPODIS 2022)},
  pages =	{22:1--22:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-265-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{253},
  editor =	{Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17642},
  URN =		{urn:nbn:de:0030-drops-176420},
  doi =		{10.4230/LIPIcs.OPODIS.2022.22},
  annote =	{Keywords: Approximate agreement on graph, wait-free solvability, triangulated sphere}
}

Keywords: Approximate agreement on graph, wait-free solvability, triangulated sphere
Collection: 26th International Conference on Principles of Distributed Systems (OPODIS 2022)
Issue Date: 2023
Date of publication: 15.02.2023

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI