Connected Sensor Cover Problem

1. Connected Sensor Cover Problem Himanshu Gupta, Samir R. Das, and Quinyi Gu, "Connected sensor cover: self-organization of sensor networks for efficient query execution," Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing (MobiHoc03), pp. 189-200, Annapolis, MD, USA, 2003. Presented By Donghyun KimJuly 2, 2008Mobile Computing and Wireless Networking Research Group at University of Texas at Dallas

2. Component • Sensor • Data Processor • Wireless Communication Module • Characteristics • Small Size • Low-cost (Ideally) • Low-Power Sensor Node Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

3. Consisted of a large number of sensor nodes. • Nodes are densely deployed either inside or near to the phenomenon (event). • Support multi-hop message exchange. • Random deployment is possible • Self-organizing capabilities • Cooperative capabilities Sensor Network Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

4. Sensing target • Temperature, humidity, vehicular movement, lightning condition, pressure, soil makeup, noise levels, and etc. • Sensor nodes can be used for • Continuous sensing, event detection, event ID, location sensing, and local control of actuators. Sensor Networks Applications Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

5. Military application • Monitoring friendly forces, equipment and ammunition • Reconnaissance of opposing forces and terrain • Nuclear, biological and chemical attack detection and reconnaissance • Battle damage assessment • Battlefield surveillance • Targeting Sensor Networks Applications – cont’ Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

6. Environmental applications • Forest fire detection • Bio-complexity mapping of the environment • Flood detection • Precision Agriculture Sensor Networks Applications – cont’ Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

7. Health applications • Tele-monitoring of physiological data • Tracking and monitoring doctors and patients inside a hospital • Drug administration in hospitals • Home applications • Home automation • Smart environment • Other commercial applications • Environmental control in office buildings • Interactive museums • Detecting and monitoring car thefts • Managing inventory control • Vehicle tracking and detection Sensor Networks Applications – cont’ Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

8. Motivation • Spatial Queries: DATA (Timestamp, Location) • Limited Battery Power Connected Sensor Cover Problem Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

9. Objectives • The sensing regions of the selected set of sensors cover the entire region of the query. • The selected set of sensors form a connected subgraph of a Disk Graph with Bidirectional link (DGB). • It is NP-Hard. • Notations • : the set of vertices • : the sensing region of . • : connected sensor cover (at the end) • : query • : target region being queried • must satisfy… • The subgraph induced by has to be connected Connected Sensor Cover Problem – cont’ Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

10. Connected Sensor Cover Problem – cont’ Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

11. A subelement is a set of points. • Two points belong to same subelementiff they are covered by the same set of sensing regions. • Given a query region , a subelement is valid if its region interescts with . Subelements and Valid Subelements Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

12. Basic Idea • is current cover. • A Candidate Sensor has an intersection with any node in and target region. • A Candidate Path is a set of nodes and it connects a node in to . • A with the highest benefit is selected and all nodes in it is added to . Greedy Algorithm Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

13. What is benefit? • Let a candidate path covers a set of uncovered valid subelements . • Then, benefit is defined as . • Objectives function • Among all possible s and corresponding s we pick and with maximum benefit. Greedy Algorithm– cont’ Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

14. Basic Idea • Based on “Charging (Weighting) Scheme”. We are going to compute how many sensors do we need to cover one sensing region at the worst case. • Partition all area into pieces with same size (sensing region), where is an optimal sensor cover. • Compute the maximum charge inside one sensing region. Denote this is . Then, the total charge is no more than and this algorithm is -approximation algorithm. Performance Analysis Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

15. When a candidate path is selected, we charge the uncovered valid subelements covered by with . • Each uncovered valid subelement gets charged by , where is the number of uncovered valid subelemets covered by . Performance Analysis – cont’ Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

16. Assume at each stage of the algorithm, some uncovered valid subelements in the sensing region get covered. • Denote be the number of uncovered valid subelements of after iteration. • is the total number of valid subelements of . • The number of valid subelements covered during the jth iteration is . • Then, assuming the loop runs of iterations, the total charge accumulated by during the entire course of the algorithm is Performance Analysis – cont’ Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

17. Link Radius • The link radius of a sensor network is defined as the maximum communication (hop) distance between any two sensor whose sensing regions interest. • Denote the maximum number of subelement is a sensing region as . Then, Performance Analysis – cont’ Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

18. Steiner Tree Based Approach • Conceptually, having the same theoretical bound. • Expected to incur more messages. • Weighted Version • Each sensor on has a weight and ’s weight is the sum of weight of sensors in it. • Objective function has to be modified accordingly. • Approximation ratio: Other Ideas Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

19. Distributed Version Presented by Donghyun Kim on July 2, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas