Abstract
Consider a pointtopoint messagepassing network. We are interested in the asynchronous crashtolerant consensus problem in incomplete networks. We study the feasibility and efficiency of approximate consensus under different restrictions on topology knowledge and the relay depth, i.e., the maximum number of hops any message can be relayed. These two constraints are common in largescale networks, and are used to avoid memory overload and network congestion respectively. Specifically, for positive integer values k and k', we consider that each node knows all its neighbors of at most khop distance (khop topology knowledge), and the relay depth is k'. We consider both directed and undirected graphs. More concretely, we answer the following question in asynchronous systems: "What is a tight condition on the underlying communication graphs for achieving approximate consensus if each node has only a khop topology knowledge and relay depth k'?" To prove that the necessary conditions presented in the paper are also sufficient, we have developed algorithms that achieve consensus in graphs satisfying those conditions:
 The first class of algorithms requires khop topology knowledge and relay depth k. Unlike prior algorithms, these algorithms do not flood the network, and each node does not need the full topology knowledge. We show how the convergence time and the message complexity of those algorithms is affected by k, providing the respective upper bounds.
 The second set of algorithms requires only onehop neighborhood knowledge, i.e., immediate incoming and outgoing neighbors, but needs to flood the network (i.e., relay depth is n, where n is the number of nodes). One result that may be of independent interest is a topology discovery mechanism to learn and "estimate" the topology in asynchronous directed networks with crash faults.
BibTeX  Entry
@InProceedings{sakavalas_et_al:LIPIcs:2018:10074,
author = {Dimitris Sakavalas and Lewis Tseng and Nitin H. Vaidya},
title = {{Effects of Topology Knowledge and Relay Depth on Asynchronous Appoximate Consensus}},
booktitle = {22nd International Conference on Principles of Distributed Systems (OPODIS 2018)},
pages = {14:114:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770989},
ISSN = {18688969},
year = {2018},
volume = {125},
editor = {Jiannong Cao and Faith Ellen and Luis Rodrigues and Bernardo Ferreira},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/10074},
URN = {urn:nbn:de:0030drops100744},
doi = {10.4230/LIPIcs.OPODIS.2018.14},
annote = {Keywords: Asynchrony, crash, consensus, incomplete graphs, topology knowledge}
}
Keywords: 

Asynchrony, crash, consensus, incomplete graphs, topology knowledge 
Collection: 

22nd International Conference on Principles of Distributed Systems (OPODIS 2018) 
Issue Date: 

2018 
Date of publication: 

15.01.2019 