Sink-Connected Barrier Coverage Optimization for Wireless Sensor Networks Jehn-Ruey Jiang National Central University Jhongli City, Taiwan

Outline Background Background Sink-Connected Barrier Coverage Optimization Problem Maximum Flow Minimum Cost Planning Performance Evaluation Conclusion 1

Virtual Barrier of Sensors 2 Wireless Sensor Network (WSN) Node

WSN: Wireless Sensor Network 3 Sensing Range Communication Range Sensor Node Sink Node

Wireless Sensor Node Examples 4 A wireless sensor node is a device integrating sensing, communication, and computation. It is usually powered by batteries.

Wireless Sensor Node Example: Octopus II 5 Developed in National Central University and National Tsin Hua University MCU: TI MSP430, 16-bit RISC microcontroller 8Mz Memory: 40KB in-system programmable flash,10KB RAM, 1MB expandable flash RF: Chipcon CC2420, 2.4 GHz (Zigbee) Transceiver (250KBps) (~450m) Sensing Module: Temperature sensor, Light sensors,Gyroscope, 3-Axis accelerometer Power: 2 AA battery + = MCU+Memory+RFSensing Module

How to define a belt region? A region between two parallel curves To form barrier coverage in belt regions Adapted from slides of Prof. Ten H. Lai 6

Crossing Paths  A crossing path (or trajectory) is a path that crosses the complete width of the belt region. Crossing paths Not crossing paths Adapted from slides of Prof. Ten H. Lai 7

k-Covered A crossing path is said to be k-covered if it intersects the sensing disks of at least k sensors. 3-covered 1-covered 0-covered Adapted from slides of Prof. Ten H. Lai 8

k-Barrier Coverage A belt region is k-barrier covered if all crossing paths are k-covered. We say that sensors form a k-barrier coverage or a barrier coverage of degree k. 1-barrier covered Not barrier covered Adapted from slides of Prof. Ten H. Lai 9

Reduced to k-connectivity problem Given a sensor network over a belt region Construct a coverage graph G(V, E)  V: sensor nodes, plus two dummy nodes S, T  E: edge (u,v) if their sensing disks overlap Region is k-barrier covered iff S and T are k-connected in G. S T Adapted from slides of Prof. Ten H. Lai 10

Literature Survey [Gage 92]: to propose the concept of barrier coverage for the first time [Kumar et al. 05, 07]: to decide whether or not a belt region is k-covered (to return 0 or 1) [Chen et al. 07]: to show a localized algorithm for detecting intruders whose trajectory is confined within a slice 11

Literature Survey [Balister et al. 07]: to estimate the reliable node density achieving s-t connectivity that a connected path exists between the two far ends (lateral sides) of the belt region [Chen et al. 08a]: to return a non-binary value for the k-coverage test [Saipulla et al. 09]: for barrier coverage of WSNs with line-based deployment [Wang and Cao 11]: for barrier coverage of camera sensor networks 12

[Gage 92] Blank Coverage: The objective is to achieve a static arrangement of elements that maximizes the detection rate of targets appearing within the coverage area. 13

[Gage 92] Barrier Coverage: The objective is to achieve a static arrangement of elements that minimizes the probability of undetected enemy penetration through the barrier. 14

[Gage 92] Sweep Coverage: The objective is to move a group of elements across a coverage area in a manner which addresses a specified balance between maximizing the number of detections per time and minimizing the number of missed detections per area. (A sweep is roughly a moving barrier.) 15

[Kumar et al. 05, 07] A castle with a moat to discourage intrusion 16

[Kumar et al. 05, 07] Define weakly/strongly k-barrier coverage Establish that sensors can not locally determine whether or not the region is k- barrier covered Prove that deciding whether a belt region is k-barrier covered can be reduced to determining whether there exist k node- disjoint paths between a pair of vertices Establish the optimal deployment pattern to achieve k-barrier coverage when deploying sensors deterministically. 17

[Chen et al. 07] It introduces the concept of L-local barrier coverage, which guarantees the detection of all crossing paths whose trajectory is confined to a slice (of length L) of the belt region of deployment. 18

[Chen et al. 07] For a positive number L and a positive integer k, a belt region is said to be L-local k-barrier covered if every L-zone in the region is k-barrier covered. Theorem: Consider a rectangular belt with at least one active sensor node. If 2d-zone(u) for every active node u is k-barrier covered for some d > r, then the entire belt is L-local k-barrier covered, with L = max { 2d − 2r, d + r }. 19

[Wang and Cao 11] An object is full-view covered if there is always a camera to cover it no matter which direction it faces and the camera’s viewing direction is sufficiently close to the object’s facing direction. 20

Outline Background Sink-Connected Barrier Coverage Optimization Problem Sink-Connected Barrier Coverage Optimization Problem Maximum Flow Minimum Cost Planning Performance Evaluation Conclusion 21

Sink Connected Barrier Coverage 22

Sink Connected Barrier Coverage Optimization For a randomly deployed WSN over a belt region, we want to (1)maximize the degree of barrier coverage with the minimum number of detecting nodes (2)minimize the number of forwarding nodes that make detecting nodes sink- connected

Assumptions Sensor nodes are randomly deployed. Every sensor node can pin point its location, discover its neighbors, and report all the information to one of the sink nodes. The sink can communicate with the backend system, which is assumed to have unlimited power supply and enormous computing capacity to gather all sensor nodes’ information and perform the optimization computation. 24

Network Models Coverage Graph Gc Transmission Graph Gt 25

Coverage Graph (Gc) Coverage Graph Gc=(Vs  {S, T}, Ec) is a directed graph to represent sensing area coverage overlap relationships. Dummy nodes S and T are associated with the lateral sides. Edges (Ni, Nj) and (Nj, Ni) are in Ec, if Ni’s coverage and Nj’s coverage have overlap. A path from S to T is called a traversable path. Ni Nj 26 S T N5N5 N6N6 N7N7 N8N8 N3N3 N4N4 Outer Side Inner Side Lateral Side N 13 N9N9 N2N2 N1N1

Transmission Graph (Gt) Transmission Graph Gt=(Vs  Vk, Et) is a directed graph to represent transmission relationship. An edge (Ni, Nj)  Et, if Ni can successfully transmit data to Nj. A set S of nodes is sink-connected if there exists a path for each node in S going through only nodes in S to a sink node. 27

Sink-Connected Barrier Coverage Optimization Problem Objective 1: To find a minimum detecting node set Vd such that the number of node-disjoint traversable paths of Vd is maximized Objective 2: To find a minimum forwarding node set Vf such that (Vd ⋂ Vf=  ) and (Vd  Vf) satisfies the sink-connected property. 28 : detecting node : forwarding node : inactive node

Outline Background Sink-Connected Barrier Coverage Optimization Problem Maximum Flow Minimum Cost Planning Maximum Flow Minimum Cost Planning Performance Evaluation Conclusion 29

Problem Solving We propose an algorithm called Optimal Node Selection Algorithm (ONSA) for solving the sink-connected barrier coverage optimization problem on the basis of the Maximum Flow Minimum Cost (MFMC) planning. 30

Maximum Flow Minimum Cost Planning (1/2) Maximum Flow Minimum Cost (MFMC) planning  Given a flow network (graph) of edges with associated (capacity, cost) parameters  To find MFMC flow plan from s to t, such that: The number of flow is maximized The total cost is minimized $2 $1 $3 $1 $2 $1 flow value for MFMC planning capacity “path” and “flow” will be used alternatively 31

Maximum Flow Minimum Cost Planning (2/2) Advantage: olynomial time: O(V  E 2  log V)  Solving the problem in polynomial time: O(V  E 2  log V) Challenges in design  How to transform graphs into flow networks such that maximum flow  maximum # of disjoint paths minimum cost  minimum # of nodes 32

ONSA Goal 1 To find Flow Plan Fc to select detecting nodes in coverage graph Gc, with flows being disjoint, such that  The number of flows is maximized  The number of detecting nodes is minimized 33 Challenge 1: How to guarantee ? S T N5N5 N6N6 N7N7 N8N8 N3N3 N4N4 Outer Side Inner Side Lateral Side N 13 N9N9 N2N2 N1N1

ONSA Challenge 1 Step 1: Construct Gc Step 2: Execute node-disjoint transformation to convert Gc into the new graph Gc* Step 3: Process nodes S and T Node-Disjoint Transformation 34 Cost=0 X X'' X' Capacity=1

Node-Disjoint Transformation Example 35 N1'N1' N 1 '' N9'N9' N 9 '' S N4N4 N2'N2' N 3 '' N 2 '' N3'N3' N5'N5' N 5 '' N6'N6' N 6 '' N8'N8' N 8 '' N 13 '' N 13 ' N7'N7' N 7 '' T Capacity=1, Cost=0 Capacity=1, Cost=1 S T N5N5 N6N6 N7N7 N8N8 N3N3 N4N4 Outer Side Inner Side Lateral Side N 13 N9N9 N2N2 N1N1 Lateral Side

ONSA Goal 2 To find Flow Plan Ft to select forwarding nodes in transmission graph Gt such that  Every detecting nodes selected in Flow Plan Fc has a flow to a sink  The number of forwarding nodes is minimized S T 36 Challenge 2: How to guarantee ?

ONSA Challenge 2 Step 1: Construct Gt Step 2: Execute node-edge transformation to convert Gt into Gt* Step 3: Process nodes S and T 37 Node-Edge Transformation Cost=1 X X'' X' Capacity= 

Node-Edge Transformation Example 38

The Proposed Algorithm: ONSA 39

Planning Result 40

Theorems 41

Outline Background Sink-Connected Barrier Coverage Problem Optimal Node Selection Algorithm Performance Evaluation Performance Evaluation Conclusion 42

Analysis (1) The maximum flow minimum cost algorithm is actually the combination of the Edmonds- Karp algorithm [6], which is of O(V  E 2 ) time complexity for a graph of vertex set V and edge set E, and the minimum cost flow algorithm (MinCostFlow) [10], which is of O(V  E 2  log(V)) time complexity. 43

Analysis (2) The time complexity of ONSA is thus O(Vc*  E 2 c*  log(Vc*) + Vt*  E 2 t*  log(Vt*)), where Vc* (resp., Vt*) is the size of the vertex set in Gc* (resp., Gt*) and Ec* (resp., Et*) is the size of the edge set in Gc* (resp., Gt*). 44

Simulation (1) We compare ONSA with the global determination algorithm (GDA), which is proposed in [9] using the maximum flow algorithm, in the following aspects.  The number of selected nodes  Total energy consumption  Notification packet delay [9] S. Kumar, T.-H. Lai, and A. Arora, “Barrier coverage with wireless sensors,” Wireless Networks, vol. 13, pp. 817–834,

Simulation (2) 46

Simulation (3) 47 Comparisons of ONSA and GDA with 1 sink node in terms of the number of selected nodes Comparisons of ONSA and GDA with 2 sink nodes in terms of the number of selected nodes

Simulation (4) Comparisons of ONSA and GDA with 1 sink node in terms of the total energy consumption 48 Comparisons of ONSA and GDA with 2 sink nodes in terms of the total energy consumption

Simulation (5) 49 Comparisons of ONSA and GDA with 2 sink nodes in terms of the packet delay Comparisons of ONSA and GDA with 1 sink node in terms of the packet delay

Outline Background Sink-Connected Barrier Coverage Problem Optimal Node Selection Algorithm Performance Evaluation Conclusion Conclusion 50

Conclusion sink-connected barrier coverage optimization problem We address the sink-connected barrier coverage optimization problem. optimal node selection algorithm (ONSA) The optimal node selection algorithm (ONSA) is proposed to solve the problem. ONSA is optimal ONSA is optimal in the sense that it forms a maximum-degree sink-connected barrier coverage with a minimum number of detecting and forwarding nodes. polynomial time complexity ONSA is with the polynomial time complexity. 51

Related Publication Jehn-Ruey Jiang and Tzu-Ming Sung, “Energy-Efficient Coverage and Connectivity Maintenance for Wireless Sensor Networks,” Journal of Networks, Vol. 4, No. 6, pp , Yung-Liang Lai and Jehn-Ruey Jiang, “Sink-Connected Barrier Coverage Optimization for Wireless Sensor Networks,” in Proc. of 2011 International Conference on Wireless and Mobile Communications (ICWMC 2011), Jehn-Ruey Jiang and Yung-Liang Lai, “Wireless Broadcasting with Optimized Transmission Efficiency,” Journal of Information Science and Engineering (JISE), Yung-Liang Lai and Jehn-Ruey Jiang, “Broadcasting with Optimized Transmission Efficiency in 3-Dimensional Wireless Networks,” International Journal of Ad Hoc and Ubiquitous Computing (IJAHUC),

Thanks for your listening! 53