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cal analysis of the proliferation of polluted data in a P2P network. In their
model, peers are classified into two types: attackers and benign peers. The
former injects polluted data in the network while the latter might inadver-
tently download them. Here, a complete file is considered as an atomic unit
of data. Thus, a downloaded file can either be considered as corrupted and
cannot be used, or be considered good as a whole. Furthermore, Kumar et al.
characterize the peers' behaviors as follows:
1. As soon as a peer downloads a good file, it stops searching for the file.
2. If a peer finds a downloaded file is corrupted, it deletes the file and then
searches again. (Kumar et al. also considered the case where the peer
stops searching after a number of unsuccessful downloads.)
3. After a peer has got a good file, it makes the file available indefinitely in
the network. (Kumar et al. also considered the case where the peer just
leaves the system without contributing the good file, i.e., free-loading.)
4. All peers are homogeneous.
Peers' downloading actions are modeled stochastically. That is, a peer
selects a certain version v of a file with a probability, denoted as q
v
(t), which
is a time-varying quantity. In general, this probability is a function of the
availability of different versions and how many copies of each exist at a given
time in the network, i.e.,
q
v
(t) = f
v
(n
u
(t), u∈V (t)), v∈V (t)
(7.1)
where n
u
(t) is the number of copies of version u, V (t) is the set of different
versions of the file, and f
v
(.) is a function such that
v∈V (t)
q
v
(t) = 1.
Under this framework, Kumar et al. considered two different downloading
behaviors:
Copy Centric Downloading. In this situation, a peer just randomly
chooses a certain copy of the file to download, without regard to its
version. Thus, the probability function can be expressed as:
n
v
(t)
q
v
(t) =
u∈V (t)
n
u
(t)
(7.2)
Version Centric Downloading. In this situation, a peer is sensitive to dif-
ferent versions that exist in the network, and chooses a particular version
at random to download. Thus, the probability function can be expressed
as:
1
|V (t)|
q
v
(t) =
(7.3)
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