konstantin avrachenkov (inria) prithwish basu (bbn) giovanni neglia (inria) bruno ribeiro (cmu) don...
TRANSCRIPT
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Pay Few, Influence Most: Online Myopic Network
CoveringKonstantin Avrachenkov (INRIA)
Prithwish Basu (BBN)Giovanni Neglia (INRIA)Bruno Ribeiro (CMU)
Don Towsley (UMass Amherst)
K. Avrachenkov, P. Basu, G. Neglia, B. Ribeiro*, and D. Towsley, Pay Few, Influence Most: Online Myopic Network Covering, IEEE NetSciCom Workshop 2014 * corresponding author
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Voter Boost on Facebook: Apps targeting
supporters
1. Ask campaign contributions (volunteer time,
money, etc.)
2. Remind users (recruited nodes) & friends to vote
3. Access to friends list
Motivation: Social Networks in Political Campaigns
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Myopic Recruitment Problem
covered friend
recruited user
Problem: Find largest cover given budget B
Each recruitment has unit cost
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Common solutions:
Minimum Dominating Set (MDS)◦ NO. Dominating Set must be connected
Minimum Connected Dominating Set (MCDS)◦ Dominating Set is connected
If Topology Was Known
REAL-WORLD PROBLEM:
TOPOLOGY UNKNOWN
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Prioritize invitations without friend degree information
Online algorithm
Myopic app invitations
covered friend
recruited user
unknown node
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Existing approaches & shortcomings
MEED & MOD
Conclusions
Outline
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Existing approaches & shortcomings
MEED & MOD
Conclusions
Outline
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Breadth-first Search (BFS)
BFS explores nodes in order of discovery
FIFO queue priority
L M N
O P
G
QH JI K
FED
B C
A
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Oracle:(Guha and Khuller’ 98) greedy cover w/known topology
BFS Problem: you and your friends have many friends in common (transitivity, cluster)
Cover Performance of BFS
Wiki-talk
Slashdot
Details in the paper
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Depth-first Search (DFS)
DFS chooses random unvisited neighbor
LIFO queue priority
Avoids “cluster” overexploration
L M N O
P
G
Q
HJ
I K
FED
B C
A
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Oracle:(Guha and Khuller’ 98) greedy cover w/known topology
DFS Problem: ◦First observed
nodes are hubs◦Hubs go to
bottom of LIFO queue
Cover Performance of DFS
Wiki-talk
Slashdot
Details in the paper
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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RW chooses random
neighbor
No cost of “revisiting”
node
Random queue priority
Stateless Search (RW)
L M N O
P
G
Q
HJ
I K
FED
B C
A
Random Walk (RW) Search
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Oracle:(Guha and Khuller’ 98) greedy cover w/known topology
RW advantages: ◦ Less “cluster”
problem than BFS◦ Seeks hubs unlike
DFS
RW Problem: random priority not targeting potential super-hubs
Wiki-talk
Slashdot
Cover Performance of RW
Details in the paper
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Existing approaches & shortcomings
MEED & MOD
Conclusions
Outline
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Enron email network
Targeting “Super-hubs”
Mathematical analysis MUST consider finite
graph effects
Details in Tech Report
Avg ex. degree unrecruited
Avg ex. degree unrecruited nodewith 4 recruited friends
Avg ex. degree unrecruited nodewith 2 recruited friends
Avg ex. degree unrecruited nodewith 1 recruited friend
Budget spent so far
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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(Guha and Kuller’98) myopic heuristic1. Start tree T = {v}
2. Select neighbors of T with max excess degree
3. Add node to T
4. GOTO 2 until budget exhausted
MEED heuristic: Replaces “with max excess degree” by “with max EXPECTED excess degree”
MEED (Maximum Expected Excess Degree)
Excess degree (uncovered degree)
Assumes knowntopology
Details in the paper
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Chooses node with max recruited neighbors
MOD heuristic1.Select unrecruited w/ max recruited neighbors
2.Invite node
3.GOTO 1 until budget is exhausted
In some topologies:node max excess degree = node most recruited friends◦ e.g., (finite!) random power law graphs with α∊{1,2}◦ approx. true for Erdös-Rényi graphs
Maximum Observed Degree (MOD)
Details in the paper
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Oracle:(Guha and Khuller’ 98) greedy cover w/known topology
MOD heuristic: closer to Oracle in all tested social networks
Slashdot
Wiki-talk
Cover Performance of MOD
Details in the paper
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Amazon product-product recommendation network
Anti-social counter-example
Same nodes, same degrees +
randomized neighbors
Budget
Budget
Details in the paper
(Maiya & Berger- Wolf, KDD’11)
concluded DFS best heuristic for
most networks?!?
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Existing approaches & shortcomings
MEED & MOD
Conclusions
Outline
(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro
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Myopic Pay-to-cover problems: many open problems with real-world applications◦ Theory must consider finite networks!
Our work: Observations in social networks◦ Theory: Analysis of finite networks
◦ Empirical + why: DFS consistently bad BFS suffers with clustering RW better than BFS MOD better overall
Thank you! Tech report @ http://www.cs.cmu.edu/~ribeiro
Conclusions