lidong.wu@utdallas

1. Small Sensor, Big Data • Ding-Zhu Du • University of Texas at Dallas lidong.wu@utdallas.edu

2. Small Sensor and Big Data • Lidong Wu • University of Texas at Dallas lidong.wu@utdallas.edu

3. Digitized World Drowning in Vast Amount of Data BigData Sensor

4. Outline • Data Collection in Sensor System • Data Analysis on Social Networks • Kate Middleton Effect, Search cheap ticket • Final Remarks

5. Outline • Data Collection in Sensor System • Data Analysis on Social Networks • Kate Middleton Effect, Search cheap ticket • Final Remarks

6. Have you watched movie Twister? tornado Bucket of sensors sensor

7. Where are all the sensors? • Smartphone with a dozen of sensors

8. Where are all the sensors? • Wearable devices • - Google Glass, Apple’s iWatch

9. Where are all the sensors? • Buildings

10. Where are all the sensors? • Transportation systems, etc

11. Sensor Web • Large # of simple sensors • Usually deployed randomly • Multi-hop wireless link • Distributed routing • No infrastructure • Collect data and send it to base station

12. Applications of Senor Web

13. An example of sensor web observer

14. What’s Sensor? • Small size • Large number • Tether- less BUT…

15. What’s limiting the task? • Energy, Sense, Communication scale, CPU...

16. Challenge • Target is Covered? • Sensorsystem is Connected? Coverage & Connectivity Golden Rule, then we say System is alive!!

17. sensor target communication radius sensing radius Coverage & Connectivity Rc Rs Communication Range d ≤ Rs Sensing Range

18. sensor target communication radius sensing radius Coverage & Connectivity Rc Rs Communication Range d ≤ Rs d ≤ Rc Sensing Range

19. Min-Connected Sensor Cover Problem • A uniform set of sensors, and a target area • Find a minimum # of sensors • to meet two requirements: • [Coverage] cover the target area, and • [Connectivity] form a connected communication network. [Resource Saving] sensing disks communication network Figure: Min-CSC Problem.

20. Min-Connected Sensor Cover Problem It’s NP-hard! • Previous Work for PTAS Ο(r lnn) – approximation given by Gupta, Das and Gu [MobiHoc’03, 2003], wheren is the number of sensors and ris the link radius of the sensor network.

21. Main Results • Random algorithm: • Ο(log3n log log n)-approximation, n is the number of sensors. • Partition algorithm : • Ο(r)-approximation, ris thelink radius of the network.

22. 2 1 Algorithm 1 Connected Sensor Cover with Target Points Connected Sensor Cover with Target Area Group Steiner Tree Min-CSC Min-CTC GST With a random algorithm which with probability 1- ɛ, produces an Ο(log3n log log n) - approximation.

23. 2 1 Min-CSC Min-CTC GST

24. 2 1 Min-CSC Min-CTC GST Min-Connected Sensor Cover Problem • A uniform set of sensors, and a target area • Find a minimum # of sensors • to meet two requirements: • [Coverage] cover the target area, and • [Connectivity] form a connected communication network. How to map to GST?

25. 2 1 Min-CSC Min-CTC GST Min-Connected TargetCoverage Problem • A uniform set of sensors, and a target POINTS • Find a minimum # of sensors • to meet two requirements: • [Coverage] cover the target POINTS, and • [Connectivity] form a connected communication network. How to map to GST?

26. 2 1 Min-CSC Min-CTC GST Group Steiner Tree: • A graph G = (V, E)with positive edge weight c for every edge e ∈ E. • A specified vertex r • k subsets (or groups) of vertices G1,...,Gk, Gi ⊆ V • Find a minimum total weight tree T contains at least one vertex in each Gi. Figure: GST Problem. This tree has minimum weight.

27. Coverage b1 b2 b3 b4 b5 b6 b7 S1 S2 S3 S1 S3 S2 S3 S4 S3 S4 S2 S4 S2 S3 S1 S2 2 1 Min-CSC Min-CTC GST Choose at least one sensor from each group. S2 b1 S1 * Gicontains all sensors covering bi. b3 b5 b2 b4 b7 S4 b6 S3

28. b1 Connectivity b2 b3 b4 b5 b6 b7 S1 S2 S3 S1 S3 S2 S3 S4 S3 S4 S2 S4 S2 S3 S1 S2 2 1 Min-CSC Min-CTC GST Consider communication network. S2 b1 S1 * Gicontains all sensors covering bi. b3 b5 b2 b4 b7 S4 b6 S3

29. b1 Min- Coverage& Connectivity b2 b3 b4 b5 b6 b7 S1 S2 S3 S1 S3 S2 S3 S4 S3 S4 S2 S4 S2 S3 S1 S2 2 1 Min-CSC Min-CTC GST S2 b1 S1 Find a group Steiner tree in communication network. * Gicontains all sensors covering bi. b3 b5 b2 b4 b7 S4 b6 S3

30. 2 1 Min-CSC Min-CTC GST Garg, Konjevod and Ravi [SODA, 2000] showed with probability 1- ε an approximation solution of GROUP STEINER TREE on tree metric T is within a factor of Ο(log2 n loglogn logk) from optimal.

31. What Is Link Radius? Communication disk Sensing disk

32. Connect output of Min-TCintoMin-CTC. It can be done in Ο(r) - approximation. 2 1 Algorithm 2 Connected Sensor Cover with Target Points Connected Sensor Cover with Target Area Min-CSC Min-CTC Min-TC Refer to my paper [INFOCOM 2013’].

33. Step 2 Target Coverage There exists a polynomial-time (1 + ε)- approximation for MIN-TC. Green is an opt (TC), Orange is an approx (TC). # < (1+ε) · opt (TC), < (1+ε) · opt (CTC)

34. Step 2 Network Steiner Tree Let S′ ⊆ S be a (1 + ε)-approximation for MIN-TC. Assign weight oneto every edge of G. Interconnect sensors in S′ to compute a Steiner tree T as network Steiner minimum tree. Byrka et al. [6] showed there exists a polynomial-time1.39-approximationof for Network Steiner Minimum Tree. Red is an approx (TC). Green is an opt (Network ST), All sensors on the tree form an approx for min CTC. # nodes % approx for min CTC = # edges +1 % approx for Network ST < 1.39 · opt (Network ST) +1 < 1.39 · ??? · opt (CTC) + 1

35. Note: # < (1+ε) · opt (CTC) Step 2 Network Steiner Tree Yellow is an approx (TC). Green is an opt (CTC). Each orange line has distance < r. opt (Network ST) < opt (CTC) -1 + r· # = opt (CTC) · O(r)

36. Future Works Ο(log3n log log n) n is the number of sensors. Ο(r) r is the link radius. 1. Unknown Relationship? 2. Constant-appro for Min-CSC?

37. What I have done? PublicationsonOptimization • “Constant-Approximations for Target Coverage Problem in Wireless Sensor Networks” INFOCOM2012 (with Weili Wu, et al.) • “Approximations for Minimum Connected Sensor Cover” INFOCOM2013(with Weili Wu, et al.) • “PTAS for Routing-Cost Constrained Minimum Connected Dominating Sets …” Journal of Combinatorial Optimization, 2013 (with Weili Wu, et al.) • “An Approximation Algorithm for Client Assignment …” INFOCOM2014 (with Weili Wu, et al.)

38. NSF Support Abovework was supported under the following grants • CCF 0829993: Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments • CNS 1018320: Undersea Sensor Networks for Intrusion Detection: Foundations and Practice • CNS 0831579: Throughput Optimization in Wireless Mesh Sensor Networks

39. Outline • Data Collection in Sensor System • Data Analysis On Social Networks • Kate Middleton Effect, Search cheap ticket • Final Remarks

40. “The small world network is a type of mathematical graph in which most nodes are not neighbors of one another, but most nodes can be reached from every other by a small number of hops or steps.”

41. Social Network: A New Frontier Most of social networks are small world networks with large size.

42. Six Steps of Separation Milgram (1967) • The experiment: • Random people from Nebraska were to send a letter (via intermediaries) to a stock broker in Boston. • Could only send to someone with whom they know. • Among the letters that found • the target, the average number of steps was six. Stanley Milgram (1933-1984) It’s a small world after all!!!

43. Six Steps of Separation Friend Friend Roommate Family Friend Interviewer Supervisor Friend Family Friend

44. Social Networks in Life

45. Increasing Popularity

46. “Kate Middleton Effect The trend effect that Kate, Duchess of Cambridge has on others, from cosmetic surgery for brides, to sales of coral-colored jeans.” Usage Example 1

47. Hike in Sales of Special Products • According to Newsweek, "The Kate Effect may be worth £1 billion to the UK fashion industry." • Tony DiMasso, L. K. Bennett’s US president, stated in 2012, "...when she does wear something, it always seems to go on a waiting list."

48. How to Find Kate? • Influential Person • Kate is one of the persons that have many friends in this social network. For more kates, it’s not as easy as you might think!

49. Find More Kate? • Challenge: an overall consideration of influence • For example, Positive Influence, Influence Maximization, Influence Minimization

50. Influence Maximization • Given k • Find k seeds (Kates) • to maximize the number of influenced persons.