Is spamming an efficient strategy in temporal networks ?
Martin Gueuning & Jean-Charles Delvenne & Renaud Lambiotte
UCLouvain & UNamur
September 2014
Dynamics On and Of Complex Networks VII
Satellite Meeting ECCS’14
Martin Gueuning ( UCLouvain & UNamur )
DOOCN VII
September 2014
1 / 11
Context
• Someone wants to spread opinion/information to his neighborhood.
• Fixed allocated time to spend between diffusing and convincing.
Martin Gueuning ( UCLouvain & UNamur )
DOOCN VII
September 2014
2 / 11
Framework
• SI diffusion model over an edge.
• power-law inter-contact probability distribution function (pdf) f (bursty
behaviour).
• Probability p of success for each attempt
−→ underlying inter-success pdf.
τ
T
T ∼ ψ(T )
τ ∼ f (τ )
Martin Gueuning ( UCLouvain & UNamur )
DOOCN VII
September 2014
3 / 11
Moments of the inter-success pdf
hT i =
2
T
k
τ =
Z
+∞
=
2
τ
1−p
+
hτ i
2 hτ i
p
3
τ
1 − p 2 (1 − p)
2
+
2 τ +
hτ i
3 hτ i
p
p
τ k f (τ ) dτ is the k th moment of the inter-contact pdf f .
0
Martin Gueuning ( UCLouvain & UNamur )
DOOCN VII
September 2014
4 / 11
Average Relay Time
Trelay
Trelay
=
1+p
2
τ
2
2 hτ i
!
−1
• Inter-meeting time pdf matters to determine whether process is bursty or not
• Probability of success p modulates the ’amplitude’ of the burstiness
Martin Gueuning ( UCLouvain & UNamur )
DOOCN VII
September 2014
5 / 11
Comparison of strategies
For a constant mean time between two successful transmissions
which is the more efficient in term of diffusion :
hτ i
p ,
increase the quantity (low hτ i)
or
increase the quality (high p) of the successive attempts ?
Martin Gueuning ( UCLouvain & UNamur )
DOOCN VII
September 2014
6 / 11
Comparison of strategies : numerical results
P for <τ>/p =cste, µ=1
At constant ratio,
higher p is more efficient in
terms of diffusion.
1
0.8
P
0.6
0.4
cst=0.5
cst=1
cst=2
cst=10
0.2
0
0
0.2
0.4
0.6
0.8
p
Martin Gueuning ( UCLouvain & UNamur )
DOOCN VII
1
p= probability of success
P= overal probability of
success before recovery
hτ i
p = naive mean time for
success
September 2014
7 / 11
Comparison of strategies : numerical results
Transmissibility P for µ=1
5
0.9
0.8
0.7
<τ>
0.6
0.5
0.4
0.3
It is more efficient to be
k times more
convincing
on
one contact than
the other way
round.
0.2
0.1
0.05
0
1
p
Martin Gueuning ( UCLouvain & UNamur )
DOOCN VII
September 2014
8 / 11
Comparison with Poisson behaviour : numerical results
Transmissibility P for bursty meeting
1
<τ>
5
0.5
0.05
0
1
0
If the meeting
dynamic
is
bursty, transmissibility
is
more sensitive
to the probability p of one
attempt.
p
Transmissibility P for Poissonian meeting
1
<τ>
5
0.5
0.05
0
1
If the meeting
dynamic
is
Poissonian,
only the ratio
matters.
0
p
Martin Gueuning ( UCLouvain & UNamur )
DOOCN VII
September 2014
9 / 11
Comparison with Poisson behaviour : numerical results
Transmissibility P for bursty meeting
5
0.8
<τ>
0.6
0.4
0.2
0.05
0
1
If the meeting
dynamic
is
bursty, transmissibility
is
more sensitive
to the probability p of one
attempt.
p
Transmissibility P for Poissonian meeting
5
0.8
<τ>
0.6
0.4
0.2
0.05
0
If the meeting
dynamic
is
Poissonian,
only the ratio
matters.
1
p
Martin Gueuning ( UCLouvain & UNamur )
DOOCN VII
September 2014
10 / 11
Conclusion
• Distinction between inter-meeting and underlying diffusive processes
• Integration of social (burstiness) and ’biological’ (probability of success)
factors
Facing bursty meeting interactions, favor the quality of your message !
Martin Gueuning ( UCLouvain & UNamur )
DOOCN VII
September 2014
11 / 11