  We consider the problem of distributed corruption detection in networks. In
this model, each vertex of a directed graph is either truthful or corrupt. Each
vertex 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
\emph{all} corrupt (that is, faulty) vertices can be identified, when there is
a known upper bound on their number.
  We are interested in networks in which the identity of a \emph{large
fraction} of the vertices can be identified.
  It is known that in the PMC model, in order to identify all corrupt vertices
when their number is $t$, all indegrees 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 vertices, and a $1-O(1/d)$ fraction of the
truthful vertices can be identified, whenever there is a majority of truthful
vertices. We also observe that if the graph is very far from being a good
expander, namely, if the deletion of a small set of vertices splits the graph
into small components, then no corruption detection is possible even if most of
the vertices are truthful. Finally, we discuss the algorithmic aspects and the
computational hardness of the problem.
