TY - JOUR
T1 - Distributed corruption detection in networks
AU - Alon, Noga
AU - Mossel, Elchanan
AU - Pemantle, Robin
N1 - Funding Information:
Research supported in part by NSF grant DMS-1855464, ISF grant 281/17, BSF grant 2018267 and the Simons Foundation. Research supported in part by NSF awards DMS-1737944, ONR N00014-16-1-2227, N00014-17-1-2598, ARO MURI W911NF1910217 and Simons Investigator award (622132). Research supported in part by NSF grant # DMS-1209117.
Funding Information:
∗Research supported in part by NSF grant DMS-1855464, ISF grant 281/17, BSF grant 2018267 and the Simons Foundation. †Research supported in part by NSF awards DMS-1737944, ONR N00014-16-1-2227, N00014-17-1-2598, ARO MURI W911NF1910217 and Simons Investigator award (622132). ‡Research supported in part by NSF grant # DMS-1209117.
Publisher Copyright:
© 2020 Noga Alon, Elchanan Mossel, and Robin Pemantle.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Distributed computing
KW - Expander graphs
KW - Graph separators
KW - Network testing
KW - PMC model
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U2 - 10.4086/toc.2020.v016a001
DO - 10.4086/toc.2020.v016a001
M3 - Article
AN - SCOPUS:85083901383
SN - 1557-2862
VL - 16
SP - 1
EP - 23
JO - Theory of Computing
JF - Theory of Computing
IS - 1
ER -