1. │ University of Texas at Dallas │
Lecture 3-1
Profit Maximization
Ding-Zhu Du
│ University of Texas at Dallas │
Social network analysis [SNA] is the mapping and measuring of relationships and flows between people, groups, organizations, computers or other information/knowledge processing entities.
The nodes in the network are the people and groups while the links show relationships or flows between the nodes.
The advantage of social network analysis is that, unlike many other methods, it focuses on interaction (rather than on individual behavior).
Network analysis allows us to examine how the configuration of networks influences how individuals and groups, organizations, or systems function.

2. Optimization in Social Networks
PhD Dissertation:
Optimization in Social Networks
-Influence and Profit
Candidate: Yuqing Zhu
Advised by Prof. Weili Wu and Prof. Ding-Zhu Du
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3. 13th IEEE International Conference on Data Mining (ICDM 2013)
Influence and Profit: Two Sides of the Coin
13th IEEE International Conference on Data Mining (ICDM 2013)
Yuqing Zhu
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4. Overview Background: Social Influence Propagation & Maximization
Influence and Profit
Proposed Model & Its Properties
BIP Maximization Algorithms
Experimental Results
Conclusions
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5. Influence in Social Networks
We live in communities and interact with friends, families, and even strangers
This forms social networks
In social interactions, people may influence each other
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6. Influence Diffusion & Viral Marketing
Word-of-mouth effect
iPad Air is great
iPad Air is great
iPad Air is great
iPad Air is great
iPad Air is great
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Source:Wei Chen’s KDD’10 slides

7. Social Network as Directed Graph
0.13
0.6
0.3
0.1
0.27
0.41
0.54
0.16
0.11
0.2
0.7
0.2
0.1
0.8
0.7
0.9
Nodes: Individuals in the network
Edges: Links/relationships between individuals
Edge weight on : Influence weight
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8. Linear Threshold (LT) Model – Definition
Each node chooses an activation threshold uniformly at random from [0,1]
Time unfolds in discrete steps 0,1,2…
At step 0, a set 𝑆of seeds are activated
At any step , activate node if
The diffusion stops when no more nodes can be activated
Influence spread of 𝑆:The expected number of active nodes by the end of the diffusion, when targeting 𝑆 initially
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9. Linear Threshold(LT) Model – Exampley
Inactive Node
0.6
Active Node
0.2
0.2
0.3 x
Threshold
0.1
Total Influence Weights
0.4 U
0.3
0.5
0.2
Stop!
0.5 w v
Influence spread of {v} is 4
Source: David Kempe’s slides
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10. Independent Cascade (IC) Model – Definition
is the probability of success when tries to activate
Time unfolds in discrete steps 0,1,2…
At step 0, a set 𝑆 of seeds are activated
At any step , a newly activated node has one chance to active its out-neighbor , with probability
The diffusion stops when no more nodes can be activated
Influence spread of 𝑆:The expected number of active nodes by the end of the diffusion, when targeting 𝑆initially
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11. Independent Cascade(IC) Model – Exampley
Inactive Node
0.6
Active Node
0.2
0.2
0.3 x
Threshold
0.1
Total Influence Weights
0.4 U
0.3
0.5
0.2
Stop!
0.5 w v
Influence spread of {v} is 4
Source: David Kempe’s slides
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12. Influence Maximization
Problem
Select k individuals such that by activating them, influence spread is maximized.
Input
NP-hard 
#P-hard to compute exact influence 
Output
A directed graph representing a social network, with influence weights on edges
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13. Influence and Profit
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14. Influence vs. Profit
Classical models do not fully capture monetary aspects of
product adoptions
Being influenced Being willing to purchase
Classical models do not consider the willingness the active nodes on spreading the influence
Being influenced Being willing to spread the influence
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15. Influence vs. Profit Influence: Profit:
In market, a famous company does not always make generous profit. E.g. Twitter, SONY, Weibo
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16. Product Adoption Product adoption is a two-stage process (Kalish 85)
1st stage: Awareness
Get exposed to the product
Become familiar with its features
2nd stage: Actual adoption
Only if valuation outweighs price
Only in this case the company gains real profit
The 2nd stage is not captured in existing work
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17. Valuations for Products
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18. Our Contribution Price-Related (PR) Frame
Incorporate monetary aspects to model the willingness of the nodes on spreading influence
Price-Related (PR) Frame
PR-L model LT model
PR-I model IC model
Balanced Influence and Profit (BIP) Maximization Problem
Two Marketing Strategies:
BinarY priCing (BYC)
PAnoramic Pricing (PAP)
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19. Proposed Model & Problem Definition
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20. Price Related (PR) Frame
Rules in IC or LT
Neutral
Influenced
Active
Three node states: Neutral, Influenced, and Active
Neutral Influenced: same as in LT or IC
Influenced  Active: Only if the valuation is at least the quoted price
Only active nodes will propagate influence to inactive neighbors
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21. Pricing Strategies BinarY priCing (BYC) PAnoramic Pricing (PAP)
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22. BIP: Notations : the vector of quoted prices, one per each node
: the vector of quoted prices, one per
each node
: the seed set
R: the influence function
:the expected influence earned by targeting and setting prices
R: the profit function
:the expected profit earned by targeting and setting prices
: the objective function of balanced Influence and Profit problem
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23. BIPMax Problem Definition
Input
Problem
Select a set of seeds & determine a vector of quoted price, such that the is maximized under the PR Frame
Output
A directed graph representing a social network, with influence weights on edges
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24. BIPMax vs. InfMax Difference w/ InfMax under LT/IC
Propagation models are different & have distinct properties
InfMax only requires “binary decision” on nodes, while BIPMax requires to set prices
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25. A Restricted Special Case
Simplifying assumptions:
Valuation:
Pricing: BYC (Seeds get the item for free)
Every seed will automatically adopt the product and propagate the influence
Optimal price vector is out of question
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26. A Restricted Special Case
: The uniform price for every non-seed
: production cost
max:
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27. A Restricted Special Case
Theorem 1: Under PR-I model, when , maximizing B(S) is in P (can be solved in polynomial time).
Equivalent to: how to find the minimum set of nodes such that there is a path from this set to each node in this graph.
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28. Theorem 1:
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29. A Restricted Special Case
Theorem 2: Under PR-I model, when , maximizing B(S) is NP-hard.
Reduction from the Set Cover problem
Theorem 3: Under PR-L model, for any , maximizing B(S) is NP-hard.
Reduction from the Vertex Cover problem
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30. u1 s1 v1 u2 s2 u3 v2 v3 v4 s3 u4 v5 s4 u5 v6 v7 u6 v8 u7
Set Cover problem.
Vertex Cover problem.
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31. … … … … … … … Theorem 2: Reduction from the Set Cover problem.
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32. … … … …
Theorem 3: Reduction from the Vertex Cover problem.
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33. Algorithms for BIP Maximization
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34. BIPMax Algorithms Given the distribution function (CDF) of . Define:
the Optimal Price is
Define:
Myopic: Ignores network structures and “profit potential” (from influence) of seeds
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35. Determining the Seeds and Prices under BYC
Assign all the nodes a uniform price :
Pick the node that brings the maximum profit:
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36. Determining the Seeds and Prices under PAP
Two possible results after offering price to :
accepts, The influence collected from is 1 and the profit is
does not accept, The influence collected from it is 1 and the profit is 0.
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37. Determining the Seeds and Prices under PAP
BIP Margin Profit: :
Define:
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38. Determining the Seeds and Prices under PAP
Assign each the node the myopic price :
Decide the new price to maximize BIP:
Pick the node that brings the maximum profit with its new price :
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39. Distribution of User’s Valuation
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40. Experiments: Datasets & Results
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41. Network Datasets Enron Epinions NetHEPT
A dataset from about the users who mostly are senior managements of Enron.com
Epinions
A who-trusts-whom network from the customer reviews site
Epinions.com
NetHEPT
A co-authorship network from arxiv.org High Energey Physics Theory section.
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42. Network Datasets
Statistics of the datasets:
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43. Experimental Results:
Influence and profit of trivalency PR-I on NetHept
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44. Experimental Results:
Influence and profit of weighted cascade PR-I on Epinion
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45. Experimental Results: Price Assignment for Seeds
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46. Experimental Results: Profit comparison of APAP and PAGE
Experimental Results: Running time on weighted cascade PR-I graph
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47. Conclusions
Extended LT and IC model to incorporate price and valuations & distinguish product adoption from social influence
Studies the properties of the extended model
Proposed Balanced Influence and Profit maximization (BIPMax) problem & effective algorithm to solve it
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48. Future Work
Approximation algorithm design for this problem, approximation ratio and inapproximability.
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49. Future Work
Scalable algorithms of mining the profit and influence in large-scale social networks, e.g., consider the simpler network structure like arborescence and directed acyclic graph.
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50. Publications
Book Chapter [1] Lidong Wu, Weili Wu, Zaixin Lu, Yuqing Zhu, and Ding-Zhu Du, “Sensor Cover and Double Partition”, Springer Proceedings in Mathematics & Statistics Volume 59, 2013, pp Conference Papers [2] Yuqing Zhu, Weili Wu, Deying Li, and Hui Xiong, “Multi-Influence Maximization in Competitive Social Networks,” submitted to the 20th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD 2014). [3] Yuqing Zhu, Yiwei Jiang, Weili Wu, Ling Ding, Ankur Teredesai, Deying Li, and Wonjun Lee, “Minimizing Makespan and Total Completion Time in MapReduce-like Systems,” accepted by the 33rd IEEE International Conference on Computer Communications (INFOCOM 2014). [4] Yuqing Zhu, Weili Wu, James Willson, Ling Ding, Lidong Wu, Deying Li, and WonJun Lee, “An Approximation Algorithm for Client Assignment in Client/Server Systems”, accepted by the 33rd IEEE International Conference on Computer Communications (INFOCOM 2014). [5] Yuqing Zhu, Zaixin Lu, Yuanjun Bi, Weili Wu, Yiwei Jiang, and Deying Li, “Influence and Profit: Two sides of the coin,” accepted by IEEE International Conference on Data Mining (ICDM 2013). [6] Yuqing Zhu, Weili Wu, Lidong Wu, Li Wang, and Jie Wang, “SmartPrint: A Cloud Print System for Office”, accepted by IEEE International Conference on Mobile Ad-hoc and Sensor Networks (MSN 2013). [7] Lirong Xue, Donghyun Kim, Yuqing Zhu, Deying Li, Wei Wang, and Alade Tokuta, “A New Approximation Algorithm for Multiple Data Ferry Trajectory Planning Problem in Heterogenous Wireless Sensor Networks”, accepted by the 33rd IEEE International Conference on Computer Communications (INFOCOM 2014). [8] Yuanjun Bi, Weili Wu, and Yuqing Zhu, “CSI: Charged System Influence Model for Human Behavior Prediction,” accepted by IEEE International Conference on Data Mining (ICDM 2013).
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51. [9] Songsong Li, Yuqing Zhu, Deying Li, Donghyum Kim, Huan Ma, and Weili Wu, “Influence Maximization in Social Networks with User Attitude Modification”, accepted by the IEEE International Conference on Communications (ICC 2014).
[10] Huan Ma, Zaixin Lu, Lidan Fan, Weili Wu, Deying Li, and Yuqing Zhu, “A Nash Equilibrium Based Algorithm for Mining Hidden Links in Social Networks”, accepted by International Conference on Combinatorial Optimization and Applications (COCOA 2013).
[11] Songsong Li, Yuqing Zhu, Deying Li, Donghyun Kim, and Hejiao Huang, “Rumor Restriction in Online Social Networks”, accepted by the 32nd IEEE International Performance Computing and Communications Conference (IPCCC 2013).
[12] Huan Ma, Yuqing Zhu, Deying Li, Wenping Chen, Zhiming Ding, Weili Wu, “Improve the Influence When Negative Opinion Emerges in Social Networks”, accepted by China Wireless Sensor Networks Conference (CWSN 2013), Excellent Paper (8 out of 200 accepted papers).
     
[13] Ling Ding, Yuqing Zhu, James Willson, Ankur Teredesai, and Peter Pentescu, “A Resource Sharing Incentive Mechanism in Mobile Cloud Computing”, submitted to IEEE International Conference on Cloud (Cloud 2014).
Journal Papers
[14] Yuqing Zhu, Weili Wu, Lidan Fan, James Willson, Ling Ding, and Deying Li, “Mutual Relationship Based Community Partitioning for Social Networks”, submitted to IEEE Transactions on Emerging Topics in Computing (TETC)
[15] Yuqing Zhu, Ling Ding, Weili Wu, and Wonjun Lee, “A Secondary User Stimulating Mechanism for Cooperative Sensing in Cognitive Radio Networks”, under the 1st revision of IEEE Transactions on Vehicular Technology (TVT).
[16] Yuqing Zhu, Weili Wu, Yuanjun Bi, Lidong Wu, Yiwei Jiang, and Wen Xu, “Better Approximation Algorithms for Influence Maximization in Online Social Networks”, accepted by Journal of Combinatorial Optimization (JOCO), 2013.
[17] Yiwei Jiang, Yuqing Zhu, Weili Wu, Deying Li, and Wonjun Lee, “Scheduling in MapReduce: To Minimize the Maximum and Total Completion Time”, submitted to IEEE Transactions on Cloud Computing (TCC)
[18] Xianling Lu, Yuqing Zhu, Deying Li, Biaofei Xu, Wenping Chen, Zhiming Ding, “Minimum Payment Collaborative Sensing Network using Mobile Phones”, accepted by Wireless Networks.
[19] Biaofei Xu, Yuqing Zhu, Deying Li, Donghyun Kim, and Weili Wu, “Minimum (k-ω)-Angle Barrier Coverage in Wireless Camera Sensor Networks”, accepted by International Journal of Sensor Networks (IJSNet), 2013.
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52. [20] Yuanjun Bi, Weili Wu, Yuqing Zhu, Lidan Fan, and Ailian Wang, “A Nature-Inspired Influence Propagation Model for the Community Expansion Problem”, accepted by Journal of Combinatorial Optimization (JOCO), [21] Xianling Lu, Deying Li, Wenping Chen, Yuqing Zhu, Hongwei Du, and Zhiming Ding, “Maximum Lifetime Temporal Q-Coverage in Directional Sensor Networks,” accepted by Ad Hoc & Sensor Wireless Networks. [22] Zaixin Lu, Yuqing Zhu, Wei Li, Weili Wu, Xiuzhen Cheng, “Influence-based Community Partition for Social Networks”, accepted by Journal of Computational Social Networks. [23] Yiwei Jiang, Jueliang Hu, Longcheng Liu, Yuqing Zhu, and T.C. Edwin. Cheng, “Competitive Ratios for Preemptive and Non-preemptive Online Scheduling with Nondecreasing Concave Machine Cost,” Information Sciences (INS), [24] Huan Ma, Yuqing Zhu, Deying Li, Songsong Li, and Weili Wu, “Loyalty Improvement beyond the Seeds in Social Networks”, accepted by Journal of Combinatorial Optimization (JOCO), [25] Deying Li, Qinghua Zhu, Yuqing Zhu, Hongwei Du, Weili Wu, and Wonjun Lee, “Conflict-free Many-to-One Data Aggregation Scheduling in Multi-channel Multi-hop Wireless Sensor Networks”, accepted by International Journal of Sensor Networks (IJSNet), [26] Yiwei Jiang, Jueliang Hu, Zewei Weng, and Yuqing Zhu, “Parallel Machine Covering with Limited Number of Preemptions”, accepted by Mathematics-A Journal of Chinese Universities, 2013 [27] Lidong Wu, Hongwei Du, Weili Wu, Yuqing Zhu, AilanWang, and Wonjun Lee, “PTAS for Routing-Cost Constrained Minimum Connected Dominating Set in Growth Bounded Graphs”, accepted by Journal of Combinatorial Optimization (JOCO) ,2013. [28] Lidan Fan, Zaixin Lu, Weili Wu, Yuanjun Bi, Yuqing Zhu, Huan Ma, and Bhavani M. Thuraisingham, “Rumor Control in Social Networks-Community Inspiration”, submitted to IEEE Transactions on Network Science and Engineering. [29] Yuqing Zhu, and Cheng Li, “The Discussion of Standardized Enterprise Decision Based on Multidimensional Data”, Information Technology & Standardization, 2007(11),
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53. Thank you!
Q&A
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