what-when-how
In Depth Tutorials and Information
∑
,
=
,
/
,
P s a
(
)
T s a
(
)
T s a
(
)
(1.2)
a
On the other hand, the second relationship is the conditional probability
P
(
A
|
s
).
P
(
A
|
s
) means that for a given torrent
s
, the likelihood of ASes
A
being used by a given
torrent
s
. his value can be computed by electing the row in the table
T
correspond-
ing to
s
, and normalize it by the sum of this row. he computing detail is shown in
Figure 6.27, and the elements distribution of table
T
are shown in Figure 6.28.
∑
, =
,
/
,
P a s
(
)
T s
(
a
)
T s a
(
)
(1.3)
s
According to these two relationships. We can further compute the probability
P
(
A
|
a
).
P
(
A
|
a
) summarizes how AS
a
is associated with all other ASes
A
due to the
torrent level relationship. By tally up how likely other ASes are also holding similar
mount of peers from the same torrent, we sum over the contribution in proportion
to how frequently torrent
s
is belonged to AS
a
.
P A a
(
|
)
=
P A s P s
(
|
)
(
|
a
)
+
P A s P s
(
|
)
(
|
a
)
+ ...
1
1
2
2
∑
s
=
|
|
P A s P s a
(
)
(
)
(1.4)
After the computing of
P
(
A
|
a
), we use entropy to quantify the mount of random-
ness in the probability distribution. Note that this value is negative; large entropy
implies AS
a
is weakly associated with a large number of ASes. his occurs when
the Ases generally do not have large AS clusters. On the other hand, when the value
of an AS is very small, the peers belonging to this AS are very likely to form a big
AS cluster. herefore, we can compute the entropy of
P
(
A
|
a
) as follows:
∑
=
|
=
ʹ
|
ʹ
|
Entropy a H P A a
( )
(
(
))
P a
(
a logP a
)
(
a
)
(1.5)
a A
ʹ∈
According to the entropy value of different Ases, a modified tracker protocol will
carry out the following selective locality process when a BT peer has arrived (Note
that the entropy of each AS is preprocessed by computing the table
T
according to
Equations 1.1-1.4; these entropy values are already existed in the trackers before
the following steps):
Step. 1
: When a peer
x
arrives, get the AS#
a
of this peer by sending the
“whois” request.
Step.2
: For a given AS#
a
, get the entropy of AS#
a
according to the results of
Equation 1.5.
