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Small Sensor, Big Data Ding-Zhu Du University of Texas at Dallas

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Small Sensor and Big Data Lidong Wu University of Texas at Dallas

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Sensor Drowning in Vast Amount of Data Digitized World BigData

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

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

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Have you watched movie Twister? sensor Bucket of sensors tornado

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Where are all the sensors? Smartphone with a dozen of sensors

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

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Buildings Where are all the sensors?

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Transportation systems, etc Where are all the sensors?

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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

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Applications of Senor Web

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observer An example of sensor web

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

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

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Challenge Target is Covered? Sensor system is Connected? Coverage & Connectivity Golden Rule, then we say System is alive!!

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

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

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Min-Connected Sensor Cover Problem Figure: Min-CSC 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] communication network sensing disks

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

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Main Results Random algorithm: Ο(log 3 n log log n)-approximation, n is the number of sensors. Partition algorithm : Ο(r)-approximation, r is the link radius of the network.

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C onnected S ensor C over with Target Area C onnected Sensor C over with T arget Points With a random algorithm which with probability 1- ɛ, produces an Ο(log 3 n log log n) - approximation. 1 Algorithm 1 G roup S teiner T ree 2 Min-CSCMin-CTCGST

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1 2 Min-CSCMin-CTCGST

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1 2 Min-CSCMin-CTCGST How to map to 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.

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1 2 Min-CSCMin-CTCGST How to map to GST? Min-Connected Target Coverage 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.

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1 2 Min-CSCMin-CTCGST 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 G 1,..., G k, G i ⊆ V Find a minimum total weight tree T contains at least one vertex in each G i. Group Steiner Tree: Figure: GST Problem. This tree has minimum weight.

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1 2 Min-CSCMin-CTCGST Choose at least one sensor from each group. Coverage b3b3 b1b1 b2b2 b6b6 b5b5 b4b4 S1S1 S2S2 S3S3 S4S4 b7b7 b2b2 b6b6 b3b3 b4b4 b1b1 b5b5 b7b7 S 1 S2 S 1 S3 S 1 S2 S 3 S 2 S3 S 2 S4 S 3 S4 * G i contains all sensors covering b i. S 2 S3 S4

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1 2 Min-CSCMin-CTCGST b3b3 b1b1 b2b2 b6b6 b5b5 b4b4 S1S1 S2S2 S3S3 S4S4 b7b7 Consider communication network. Connectivity b2b2 b6b6 b3b3 b4b4 b1b1 b5b5 b7b7 S 1 S2 S 1 S3 S 1 S2 S 3 S 2 S3 S 2 S4 S 3 S4 * G i contains all sensors covering b i. S 2 S3 S4

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1 2 Min-CSCMin-CTCGST b3b3 b1b1 b2b2 b6b6 b5b5 b4b4 S1S1 S2S2 S3S3 S4S4 b7b7 Find a group Steiner tree in communication network. Min- Coverage & Connectivity b2b2 b6b6 b3b3 b4b4 b1b1 b5b5 b7b7 S 1 S2 S 1 S3 S 1 S2 S 3 S 2 S3 S 2 S4 S 3 S4 * G i contains all sensors covering b i. S 2 S3 S4

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1 2 Min-CSCMin-CTCGST 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(log 2 n log log n log k) from optimal.

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What Is Link Radius? Communication disk Sensing disk

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C onnected S ensor C over with Target Area C onnected Sensor C over with T arget Points Connect output of Min-TC into Min-CTC. It can be done in Ο(r) - approximation. 1 Algorithm 2 2 Min-CSCMin-CTCMin-TC Refer to my paper [INFOCOM 2013’].

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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) Step 2 Target Coverage

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Byrka et al. [6] showed there exists a polynomial-time1.39- approximation of for Network Steiner Minimum Tree. Green is an opt (Network ST), Red is an approx (TC). Step 2 Network Steiner Tree Let S′ ⊆ S be a (1 + ε )-approximation for MIN-TC. Assign weight one to every edge of G. Interconnect sensors in S′ to compute a Steiner tree T as network Steiner minimum tree. 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

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

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Future Works Ο(log 3 n log log n) n is the number of sensors. 1. Unknown Relationship? 2. Constant-appro for Min-CSC? Ο(r) r is the link radius.

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“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.) What I have done? Publications on Optimization

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CCF : Reliable Spatial-Temporal Coverage with Minimum Cost in Wireless Sensor Network Deployments CNS : Undersea Sensor Networks for Intrusion Detection: Foundations and Practice CNS : Throughput Optimization in Wireless Mesh Sensor Networks NSF Support Above work was supported under the following grants

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

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“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.”

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

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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. Milgram (1967) Stanley Milgram ( ) It’s a small world after all!!! Six Steps of Separation

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

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Social Networks in Life

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Increasing Popularity

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

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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." Hike in Sales of Special Products

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

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

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

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51 Influence Maximization # of influenced nodes is 6.

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Influence Maximization 52 # of influenced nodes is 6.# of influenced nodes is 16. Influence Maximization

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“Better Approximations for Influence Maximization in Online Social Networks” Journal of Combinatorial Optimization, 2013 (with Weili Wu, et al.) Ongoing Research Initial Result

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Search Cheap Ticket Usage Example 2 There are about 28,537 commercial flights in the sky in the U.S. on any given day.

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It is a shortest path problem in a big data network. How to find cheap ticket?

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Cheap ticket-Graph AA123 AA456 AA789 Dallas Chicago

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Cheap ticket-Graph Dallas 8am 9am 1pm 9am 3pm 8am Each city has a set of startpoints and a set of endpoints. They are connected into a bipartite graph based on certain rules.

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Cheap Ticket-Graph Dallas 8am 9am 1pm 9am 3pm 8am

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Cheap Ticket-Graph Dallas 8am 9am 1pm 9am 3pm 8am

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If searching area is larger, then searching needs more time, but ticket price may be cheaper. Hard to do it in real-time Better software is needed Time VS Price Challenge

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Ongoing Research Initial Result “Social Network Path Analysis Based on HBase” CSoNet 2013 (with Weili Wu, et al.)

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

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SSS (Sensor and Sensing Systems): sensor networks with application in industrial engineering. Big Data Program: Critical Techniques and Technologies for Advancing Big Data Science & Engineering NSF Grant Possibilities In SSS Program & Big Data Program

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Research Experiences for Undergraduates (REU) program supports active research participation by undergraduate students in any area funded by NSF. REU : Verification and Validation for Software Safety (co-PI: Weili Wu) NSF Grant Possibilities In REU Program

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THANK YOU!

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Theorem Mathematical Model (II) Given a graph, find a positive influence dominating set with minimum cardinality. Positive Influence Dominating Set Problem

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Mathematical Model (I) Dominating set Positive influence dominating set

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