decentralized routing in social networks
DESCRIPTION
Slides for talk presented in Catedra Orange Network Course held in ETSIT-UPM, Madrid, November, 2012TRANSCRIPT
Geographic routing in social networks
C. Herrera, T. Couronne, Z. Smoreda, C. M. Schneider, R. M. Benito, M. C. González
very short paths exist
People were able to find them
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
What’s been done so far?network models
Real-world experiments
Simulation on network
data
Take home message
Routing in a real world network using only local information may be possible:
We need to understand the role of geography in the social links
Pretty BIG Data3 phone networks country scope during 6 month
Mutual links considered (at least one interaction per direction)
User are geo-located to their most used tower
Pretty BIG Data
1e−08 1e−07 1e−06 1e−05 1e−04 0.001 0.01 0.1 1
1 10 100 1000 10000k
P(k)
networkFrancePortugalSpain
Long distance relationships?
-1.5<α<-1
More likely short...
0.001 0.01 0.1 1
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0 10 20 30 40 50d (km)
P(d)
network●
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FrancePortugalSpain
Let’s route!“City”=province (20 Portugal, 96 France, 52 Spain)
We try to deliver the message to the city
Experiment conditions:• 60K Random pairs• Error if not delivered in 100 hops
Let’s route!“City”=province (20 Portugal, 96 France, 52 Spain)
We try to deliver the message to the city
Experiment conditions:• 60K Random pairs• Error if not delivered in 100 hops
Let’s route!Proposed methods
DFS: we don’t send to others who already got the message, in case everybody got, send back to the first person who sent us the message
GEO: send to the friend geographically closest to target
DEG: send to the best connected friend
Let’s route!
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france portugal spain
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freq
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routing−dfsrouting−dfs−degrouting−dfs−georouting−dfs−geo−deg
Let’s route!
10
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1e−04 0.001 0.01 0.1 1Error Rate
<l>
network● france
portugalspain
algorithm●
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routing−dfsrouting−dfs−georouting−dfs−degrouting−dfs−geo−deg
Let’s route!
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0.001 0.010 0.100Relative Province Size
<l>
users population●
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0.10.20.30.40.50.60.7
network●
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FrancePortugalSpain
Let’s route!“City”=municipality (305 Portugal, 3520 France, 8410 Spain)
We try to deliver the message to the city
Experiment conditions:• 60K Random pairs• Error if not delivered in 100 hops
Let’s route!
10
20
30
40
●
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1e−04 0.001 0.01 0.1 1Error Rate
<l>
network● france
portugalspain
algorithm●
●
●
●
routing−dfsrouting−dfs−degrouting−dfs−georouting−dfs−geo−deg
Let’s route!
10
20
30
40
●
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1e−04 0.001 0.01 0.1 1Error Rate
<l>
network● france
portugalspain
algorithm●
●
●
●
routing−dfsrouting−dfs−degrouting−dfs−georouting−dfs−geo−deg
Let’s route!
10
20
30
40
●
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1e−04 0.001 0.01 0.1 1Error Rate
<l>
network● france
portugalspain
algorithm●
●
●
●
routing−dfsrouting−dfs−degrouting−dfs−georouting−dfs−geo−deg
Let’s route!
10
20
30
40
●
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●
1e−04 0.001 0.01 0.1 1Error Rate
<l>
network● france
portugalspain
algorithm●
●
●
●
routing−dfsrouting−dfs−degrouting−dfs−georouting−dfs−geo−deg
Let’s route!
10
20
30
40
●
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1e−04 0.001 0.01 0.1 1Error Rate
<l>
network● france
portugalspain
algorithm●
●
●
●
routing−dfsrouting−dfs−degrouting−dfs−georouting−dfs−geo−deg
Let’s route!
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0.001 0.100Relative Province Size
<l>
network●
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FrancePortugalSpain
Relative City Size
Let’s route! IntracityMore difficult, success is reaching the target
Location is not so important
Add new criteria
COM: community vector, try to forward to the one in the same community than target (communities obtained via Louvain Method)
Paris Lisbon Madrid
0.000
0.002
0.004
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0 20 40 60 80 1000 20 40 60 80 1000 20 40 60 80 100l
P(l)
Algortihmrouting−dfsrouting−com−degrouting−dfs−degrouting−dfs−comrouting−dfs−com−degrouting−dfs−com−geo−deg
Let’s route! Intracity
Let’s route! Intracity
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30
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0.5 0.6 0.7 0.8 0.9 1.00.5 0.6 0.7 0.8 0.9 1.00.5 0.6 0.7 0.8 0.9 1.0Error Rate
<l>
Algorithm●
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routing−dfsrouting−com−degrouting−dfs−degrouting−dfs−comrouting−dfs−com−degrouting−dfs−com−geo−deg
Let’s route! Intracity
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30
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0.5 0.6 0.7 0.8 0.9 1.00.5 0.6 0.7 0.8 0.9 1.00.5 0.6 0.7 0.8 0.9 1.0Error Rate
<l>
Algorithm●
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routing−dfsrouting−com−degrouting−dfs−degrouting−dfs−comrouting−dfs−com−degrouting−dfs−com−geo−deg
Let’s route! Intracity Porto Lisboa Setúbal Braga Aveiro
Santarém Viseu Vila Real Bragança Coimbra
Viana do Castelo Leiria Évora Faro Portalegre
Castelo Branco Beja Guarda Madeira Azores
102030405060
102030405060
102030405060
102030405060
0.0 0.2 0.4 0.6 0.8 1.00.0 0.2 0.4 0.6 0.8 1.00.0 0.2 0.4 0.6 0.8 1.00.0 0.2 0.4 0.6 0.8 1.00.0 0.2 0.4 0.6 0.8 1.0Error Rate
<l>
Algorithmrouting−com−degrouting−com−geo−degrouting−dfsrouting−dfs−comrouting−dfs−com−degrouting−dfs−com−georouting−dfs−com−geo−degrouting−dfs−degrouting−dfs−geo−deg
Let’s route! Intracity
0.0
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20 30 40 50avg
err
network●
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franceportugalspain
#Nodes●
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2e+054e+056e+058e+05
level● municipality
province
Let’s route! Intracity
0.2
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0 500 1000 1500 2000 2500 3000
# Nodes u 103
E dfs<c
om<d
eg networkFrancePortugalSpain
Let’s route! Intracity
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om−d
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Let’s route! Intracity
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Population
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networkFrancePortugalSpain
Let’s route! Intracity
2
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1−
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om−d
eg
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Figure 2. Relation between our proposal and regular DFS across 468 urbannetworks
B. Generalizing results
An identical procedure has been performed for the top 100cities in each country, and additionally in all the provinces2.The reason for including provinces as well that is in bigcities usually urban areas go beyond the municipality in all3 countries. In all these 468 urban networks, previous resultsare consistent: routing-dfs-com-deg is still the better optionwith error rate 0.41 versus 0.51 in the case of includinggeographical information.
From now on, we will refer only to the routing-dfs-com-
deg. For these algorithm, results in error rate are stronglycorrelated with average length of arrived messages (0.92, seesuplementary information II-A), so we will focus on the errorrate, given the information provided by the average path lengthturns out to be redundant.
We have identified two factors with influence in the errorrate: the number of nodes size and the average degree. Thenumber of nodes positive correlated with the logarithm ofnetwork size, and the average degree dramatically increasesthe error rate if the average degree goes below 4 (see Suple-mentary Information II-B).
Since both efects overlap, we will measure the perfomanceof the algorithm compared to the perfomance of routing-dfs
which is the best one can do if no additional informationabout neighbouring nodes is provided. Figure 2 presents thevariation of the performance with network size. An interestingconclusion can be extracted: even if absolute error rate valuestend to be higher with network size, they grow slow O(log V )
while a DFS performs O(V ). This means is actually in bigurban networks where there is a bigger advantage on usingadditional information (in this case, communities and degree)to guide the network search.
2By province we will denote provincias in Spain and Portugal, and depart-
ments in France. Numbers for these divisions are 20, 52 and 96 respectively.Regarding geographical scope, the biggest distance is 120 km.
II. SUPLEMENTARY INFORMATION
A. Correlation < l > and Edfs�com�deg
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province
B. Parameters influencing Edfs�com�deg
Model R2
Edfs�com�deg
= ↵1 + ↵2V 0.18E
dfs�com�deg
= ↵1 + ↵2 log V 0.39E
dfs�com�deg
= ↵1 + ↵2 log V � ↵3hki 0.70
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E dfs−com
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Let’s route! Intracity
1
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1−E d
fs−co
m−de
g
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fs
network●
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levelmunicipalityprovince
0.92