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Sink-Connected Barrier Coverage Optimization for Wireless Sensor Networks

This paper discusses the optimization of sink-connected barrier coverage in wireless sensor networks, focusing on maximizing coverage and minimizing the number of nodes while ensuring connectivity to the sink node. Various approaches and performance evaluations are presented.

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Sink-Connected Barrier Coverage Optimization for Wireless Sensor Networks

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

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

  3. Virtual Barrier of Sensors Wireless Sensor Network (WSN) Node

  4. WSN: Wireless Sensor Network Sensing Range SinkNode Sensor Node Communication Range

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

  6. Wireless Sensor Node Example: Octopus II MCU+Memory+RF Sensing Module + = • Developed in National Central University and National TsinHua University • MCU: TI MSP430, 16-bit RISC microcontroller core @ 8Mz • Memory: 40KB in-system programmable flash,10KB RAM, 1MB expandable flash • RF: Chipcon CC2420, 2.4 GHz 802.15.4 (Zigbee) Transceiver (250KBps) (~450m) • Sensing Module: Temperature sensor, Light sensors,Gyroscope, 3-Axis accelerometer • Power: 2 AA battery

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

  8. Crossing Paths • A crossing path (or trajectory) is a path that crosses the complete width of the belt region. Crossing pathsNot crossing paths Adapted from slides of Prof. Ten H. Lai

  9. 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

  10. 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. Not barrier covered 1-barrier covered Adapted from slides of Prof. Ten H. Lai

  11. 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 iffS and T are k-connected in G. T S Adapted from slides of Prof. Ten H. Lai

  12. 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

  13. 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

  14. [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.

  15. [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.

  16. [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.)

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

  18. [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.

  19. [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.

  20. [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.

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

  22. Sink Connected Barrier Coverage

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

  24. 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.

  25. Network Models Coverage Graph Gc Transmission Graph Gt

  26. Coverage Graph (Gc) Outer Side N4 N1 N3 N2 N9 N13 T S Ni Nj N5 N7 N6 N8 LateralSide LateralSide Inner Side 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.

  27. 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.

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

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

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

  31. Maximum Flow Minimum Cost Planning (1/2) $1 $1 “path” and “flow” will be used alternatively $2 $3 $1 flow value forMFMC planning $1 • capacity $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

  32. Maximum Flow Minimum Cost Planning (2/2) • Advantage: • Solving the problem in polynomial time:O(V  E2 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

  33. Outer Side N4 N1 N3 N2 N9 N13 T S N5 N7 N6 N8 LateralSide LateralSide Inner Side ONSA Goal 1 Challenge 1: How to guarantee ? • To find Flow Plan Fcto select detecting nodes in coverage graph Gc, with flows being disjoint, such that • The number of flows is maximized • The number of detecting nodes isminimized

  34. ONSA Challenge 1 Node-Disjoint Transformation X' Capacity=1 X Cost=0 X'' 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

  35. N1' N2' N3' N4 N3'' N2'' N1'' Capacity=1, Cost=1 N9' T S N13' N9'' Capacity=1, Cost=0 N13'' N8' N7' N6' N5' N8'' N7'' N6'' N5'' Node-Disjoint Transformation Example Outer Side N1 N4 N3 N2 LateralSide N9 N13 T S LateralSide N5 N7 N6 N8 Inner Side

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

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

  38. S N4' N1' N3' N2' N4'' N1'' N3'' N2'' Capacity=, Cost=0 N9' N11' N14 N9'' N11'' N14'' Capacity=, Cost=1 T N13' N12' N10' N13'' N12'' N10'' Capacity=1, Cost=0 K1 K2 N5' N8' N7' N6' N8'' N5'' N7'' N6'' Node-Edge Transformation Example

  39. The Proposed Algorithm: ONSA

  40. Planning Result

  41. Theorems

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

  43. Analysis (1) The maximum flow minimum cost algorithm is actually the combination of the Edmonds-Karp algorithm [6], which is of O(V E2) 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E2log(V)) time complexity.

  44. Analysis (2) The time complexity of ONSA is thus O(Vc*E2c*log(Vc*) + Vt*E2t*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*).

  45. Simulation (1) [9] S. Kumar, T.-H. Lai, and A. Arora, “Barrier coverage with wireless sensors,” Wireless Networks, vol. 13, pp. 817–834, 2007. • 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

  46. Simulation (2)

  47. Simulation (3) 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

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

  49. Simulation (5) 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

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

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