Distributed corruption detection in networks
Name
v016a001.pdf
Description
Published version
Size
254.8 KB
Format
Adobe PDF
Checksum (MD5)
88a2554ef7c2a1a064beeb6478da2f40
Author(s)
Alon, N
Mossel, E
Pemantle, R
Date Issued
January 1, 2020
Journal
Theory of Computing
Publisher
Theory of Computing Exchange
Version
Final published version
Abstract
© 2020 Noga Alon, Elchanan Mossel, and Robin Pemantle. We consider the problem of distributed corruption detection in networks. In this model each node of a directed graph is either truthful or corrupt. Each node reports the type (truthful or corrupt) of each of its outneighbors. If it is truthful, it reports the truth, whereas if it is corrupt, it reports adversarially. This model, first considered by Preparata, Metze and Chien in 1967, motivated by the desire to identify the faulty components of a digital system by having the other components checking them, became known as the PMC model. The main known results for this model characterize networks in which all corrupt (that is, faulty) nodes can be identified, when there is a known upper bound on their number. We are interested in networks in which a large fraction of the nodes can be classified. It is known that in the PMC model, in order to identify all corrupt nodes when their number is t, all in-degrees have to be at least t. In contrast, we show that in d regular-graphs with strong expansion properties, a 1 − O(1/d) fraction of the corrupt nodes, and a 1 − O(1/d) fraction of the truthful nodes can be identified, whenever there is a majority of truthful nodes. We also observe that if the graph is very far from being a good expander, namely, if the deletion.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4086/toc.2020.v016a001
