Konstantin Avrachenkov (INRIA) Prithwish Basu (BBN) Giovanni Neglia (INRIA) Bruno Ribeiro (CMU) Don Towsley (UMass Amherst) 1 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: 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 2

(c) 2014, Bruno Ribeiro: 3 covered friend recruited user Problem: Find largest cover given budget B Each recruitment has unit cost

(c) 2014, Bruno Ribeiro: Common solutions:  Minimum Dominating Set (MDS) ◦ NO. Dominating Set must be connected  Minimum Connected Dominating Set (MCDS) ◦ Dominating Set is connected 4 REAL-WORLD PROBLEM: TOPOLOGY UNKNOWN

(c) 2014, Bruno Ribeiro:  Prioritize invitations without friend degree information  Online algorithm 5 covered friend recruited user unknown node

(c) 2014, Bruno Ribeiro:  Existing approaches & shortcomings  MEED & MOD  Conclusions 6

(c) 2014, Bruno Ribeiro:  Existing approaches & shortcomings  MEED & MOD  Conclusions 7

(c) 2014, Bruno Ribeiro: 8  BFS explores nodes in order of discovery  FIFO queue priority LM N OP G QH J IK FED BC A

(c) 2014, Bruno Ribeiro:  Oracle: (Guha and Khuller’ 98) greedy cover w/known topology  BFS Problem: you and your friends have many friends in common (transitivity, cluster) 9 Wiki-talk Slashdot Details in the paper

(c) 2014, Bruno Ribeiro: 10  DFS chooses random unvisited neighbor  LIFO queue priority  Avoids “cluster” overexploration LM N O P G Q H J IK F ED BC A

(c) 2014, Bruno Ribeiro:  Oracle: (Guha and Khuller’ 98) greedy cover w/known topology  DFS Problem: ◦ First observed nodes are hubs ◦ Hubs go to bottom of LIFO queue 11 Wiki-talk Slashdot Details in the paper

(c) 2014, Bruno Ribeiro:  RW chooses random neighbor  No cost of “revisiting” node  Random queue priority 12 LM N O P G Q H J IK F ED BC A Random Walk (RW) Search

(c) 2014, Bruno Ribeiro:  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 13 Wiki-talk Slashdot Details in the paper

(c) 2014, Bruno Ribeiro:  Existing approaches & shortcomings  MEED & MOD  Conclusions 14

(c) 2014, Bruno Ribeiro: Enron network 15 Mathematical analysis MUST consider finite graph effects Details in Tech Report Avg ex. degree unrecruited Avg ex. degree unrecruited node with 4 recruited friends Avg ex. degree unrecruited node with 2 recruited friends Avg ex. degree unrecruited node with 1 recruited friend Budget spent so far

(c) 2014, Bruno Ribeiro:  (Guha and Kuller’98) myopic heuristic 1. 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” 16 Excess degree (uncovered degree) Assumes known topology Details in the paper

(c) 2014, Bruno Ribeiro:  Chooses node with max recruited neighbors  MOD heuristic 1.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 17 Details in the paper

(c) 2014, Bruno Ribeiro:  Oracle: (Guha and Khuller’ 98) greedy cover w/known topology  MOD heuristic: closer to Oracle in all tested social networks 18 Slashdot Wiki-talk Details in the paper

(c) 2014, Bruno Ribeiro:  Amazon product-product recommendation network 19 Same nodes, same degrees + randomized neighbors Budget Details in the paper (Maiya & Berger- Wolf, KDD’11) concluded DFS best heuristic for most networks?!?

(c) 2014, Bruno Ribeiro:  Existing approaches & shortcomings  MEED & MOD  Conclusions 20

(c) 2014, Bruno Ribeiro:  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 21