1

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

2

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

3

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

4

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

5

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

6

Existing approaches & shortcomings

MEED & MOD

Conclusions

Outline

(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro

7

Existing approaches & shortcomings

MEED & MOD

Conclusions

Outline

(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro

8

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

9

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

10

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

11

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

12

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

13

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

14

Existing approaches & shortcomings

MEED & MOD

Conclusions

Outline

(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro

15

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

16

(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

17

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

18

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

19

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

20

Existing approaches & shortcomings

MEED & MOD

Conclusions

Outline

(c) 2014, Bruno Ribeiro: www.cs.cmu.edu/~ribeiro

21

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