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 -