Disconnected Agreement in Networks Prone to Link Failures
Bogdan S. Chlebus, Dariusz R. Kowalski, Jan Olkowski, Jedrzej, Olkowski

TL;DR
This paper studies algorithms for achieving agreement in networks with unreliable links, introducing concepts like stretch and providing algorithms with different time and message complexities based on network knowledge.
Contribution
It introduces the concept of stretch for disconnected agreement and presents algorithms with optimal and near-optimal time complexities under various assumptions.
Findings
An algorithm working in $O( ext{stretch})$ time with $O( ext{log } n)$ bits messages.
A general $n+1$ rounds algorithm with $O( ext{log } n)$ bits messages.
An optimal $O( ext{stretch})$ time algorithm with larger message size.
Abstract
We consider deterministic distributed algorithms for reaching agreement in synchronous networks of arbitrary topologies. Links are bi-directional and prone to failures while nodes stay non-faulty at all times. A faulty link may omit messages. Agreement among nodes is understood as holding in each connected component of a network obtained by removing faulty links. We call ``disconnected agreement'' the algorithmic problem of reaching such agreement. We introduce the concept of stretch, which is the number of connected components of a network, obtained by removing faulty links, minus~ plus the sum of diameters of connected components. We define the concepts of ``fast'' and ``early-stopping'' algorithms for disconnected agreement by referring to stretch. A network has nodes and links. Nodes are normally assumed to know their own names and ability to associate communication with…
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Taxonomy
TopicsDistributed systems and fault tolerance · Optimization and Search Problems · Age of Information Optimization
