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Sink-Connected Barrier Coverage Optimization for Wireless Sensor Networks
Jehn-Ruey Jiang
National Central UniversityJhongli City, Taiwan
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Outline
Background Sink-Connected Barrier Coverage
Optimization Problem Maximum Flow Minimum Cost Planning Performance Evaluation Conclusion
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Virtual Barrier of SensorsWireless Sensor Network (WSN) Node
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WSN: Wireless Sensor Network
Sensing Range
Communication Range
Sensor Node
SinkNode
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Wireless Sensor Node Examples
A wireless sensor node is a device integrating sensing, communication, and computation. It is usually powered by batteries.
Wireless Sensor Node Example: Octopus II
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• Developed in National Central University and National Tsin Hua 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
+ =
MCU+Memory+RF Sensing Module
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How to define a belt region?A region between two parallel curves
To form barrier coveragein belt regions
Adapted from slides of Prof. Ten H. Lai
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Crossing PathsA 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
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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
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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
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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, TE: 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
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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
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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
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[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.
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[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.
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[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.)
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[Kumar et al. 05, 07] A castle with a moat to discourage intrusion
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[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.
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[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.
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[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.
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Outline
Background Sink-Connected Barrier Coverage
Optimization Problem Maximum Flow Minimum Cost Planning Performance Evaluation Conclusion
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Sink Connected Barrier Coverage
Sink Connected Barrier Coverage OptimizationFor 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
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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.
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Network Models
Coverage Graph Gc
Transmission Graph Gt
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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
S T
N5 N6N7 N8
N3 N4
Outer Side
Inner Side
LateralSide
LateralSide
N13N9
N2N1
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Transmission Graph (Gt) Transmission Graph Gt=(VsVk, 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.
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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 (VdVf) satisfies the sink-connected property.
: detecting node
: forwarding node
: inactive node
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Outline
Background Sink-Connected Barrier Coverage
Optimization Problem Maximum Flow Minimum Cost Planning Performance Evaluation Conclusion
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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.
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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
$1
$1
flow value forMFMC planning
capacity
“path” and“flow” will be used alternatively
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Maximum Flow Minimum Cost Planning (2/2) Advantage:
Solving the problem in polynomial time:O(V E2 log V)
Challenges in designHow to transform graphs into flow networks
such that maximum flow maximum # of disjoint paths minimum cost minimum # of nodes
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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
Challenge 1: How to guarantee ?
S T
N5 N6N7 N8
N3N4
Outer Side
Inner Side
LateralSide
LateralSide
N13N9
N2N1
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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
Cost=0
X
X''
X' Capacity=1
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Node-Disjoint Transformation Example
N1'
N1''
N9'
N9''S
N4N2'
N3''N2''
N3'
N5'
N5''
N6'
N6''
N8'
N8''
N13''
N13'
N7'
N7''
T
Capacity=1, Cost=0
Capacity=1, Cost=1
S T
N5 N6 N7 N8
N3 N4
Outer Side
Inner Side
LateralSide
N13
N9
N2N1
LateralSide
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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
Challenge 2: How to guarantee ?
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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
Node-Edge Transformation
Cost=1
X
X''
X' Capacity=
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Node-Edge Transformation Example
T
N1'
N1''
N2'
N2''
N3'
N3''
N4'
N4''
N9'
N9''
N10'
N10''
N5'
N5''
N6'
N6''
N12'
N12''
N11'
N11''
N7'
N7''
N8'
N8''
N13'
N13''
S
N14
N14''
K1 K2
Capacity=, Cost=1
Capacity=, Cost=0
Capacity=1, Cost=0
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The Proposed Algorithm: ONSA
Optimal Node Selection Algorithm (ONSA)
Input: Vs, Vk, Ec, Et
Output: Vd and Vf
Step 1: Construct a coverage graph Gc(Vs{S,T}, Ec), where S and T are virtual nodes, and associate all edges incident to T with Capacity=1 and Cost=0, and all other edges with Capacity=1 and Cost=1.
Step 2: Execute node-disjoint transformation to transform Gc into the new graph Gc*.
Step 3: Execute the maximum flow minimum cost algorithm on Gc* to decide the minimum cost flow plan Fc, and let node set Vd, VdVs, be the set of nodes associated with Fc.
Step 4: Construct a transmission graph Gt(VsVk, Et), where each edge is with Capacity=1 and Cost=0. Add a virtual source node S and a virtual target node T into Gt.
Step 5: For each node in Vd on graph Gt, add an edge going from S to it with Capacity=1 and Cost=0. For each sink node, add an edge going from it to T with Capacity= and Cost=0.
Step 6: Execute node-edge transformation to transform Gt into Gt*.
Step 7: Execute the maximum flow minimum cost algorithm to find the minimum cost flow plan Ft on Gt*. Let Vm, VmVs, be the set of the nodes associated with Ft.
Step 8: Set Vf=Vm Vd and return Vd and Vf .
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Planning Result
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TheoremsTheorem 1
Let Gc be a coverage graph, Gc* be the graph transformed from Gc by the
node-disjoint transformation, and Fc be the minimum cost maximum flow
plan on Gc*. The node set Vd associated with Fc is the minimum set having
the maximum number of node-disjoint traversable paths on Gc.
Theorem 2
Let Gt be a transmission graph, Gt* be the graph transformed from Gt by
the node-edge transformation, and Ft be the minimum cost maximum flow
plan on Gt* with a given set Vd of detecting nodes and a given set Vk of sink
nodes. The node set Vf associated with Ft is the minimum set to make VdVf
sink-connected on Gt.
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Outline
Background Sink-Connected Barrier Coverage Problem Optimal Node Selection Algorithm Performance Evaluation Conclusion
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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(VE2log(V)) time complexity.
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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*).
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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, 2007.
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Simulation (2)Simulation Setting
Network Dimension 120m x 10m Network Interface 802.15.4 unslotted CSMA/CA Network Bandwidth 250 kbps Sensing Range 10m Transmission Range 10m
Simulation Duration 10s No. of Deployed Nodes 150, 200, 250, or 300 Traffic Type CBR (constant bit rate) Sending Frequency 1 packet/sec Packet Size 70 bytes Transmitting Power 19.8 mW Receiving Power 35.5 mW Idling Power 0.8 mW No. of Experiments 100 times/case
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Simulation (3)
150 200 250 3000
50
100
150
200
250
300ONSA GDA
Number of Deployed Sensor Nodes
Num
ber
of S
elec
ted
Nod
es
Comparisons of ONSA and GDA with 1 sink node in terms of the number of selected nodes
150 200 250 3000
50
100
150
200
250
300ONSA GDA
Number of Deployed Sensor Nodes
Num
ber
of S
elec
ted
Nod
es
Comparisons of ONSA and GDA with 2 sink nodes in terms of the number of selected nodes
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Simulation (4)
Comparisons of ONSA and GDA with 1 sink node in terms of the total energy consumption
150 200 250 3000
200
400
600
800
1000
1200
1400
1600
1800
2000ONSA (1 source)GDA (1 source)ONSA (2 sources)GDA (2 sources)
Number of Deployed Sensor Nodes
Tot
al E
nerg
y C
onsu
mpt
ion
(mj)
150 200 250 3000
200
400
600
800
1000
1200
1400
1600
1800
2000
ONSA (1 source)GDA (1 source)ONSA (2 sources)
Number of Deployed Sensor Nodes
Tot
al E
nerg
y C
onsu
mpt
ion
(mj)
Comparisons of ONSA and GDA with 2 sink nodes in terms of the total energy consumption
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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
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Outline
Background Sink-Connected Barrier Coverage Problem Optimal Node Selection Algorithm Performance Evaluation Conclusion
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Conclusion We address the sink-connected barrier
coverage optimization problem. The optimal node selection algorithm
(ONSA) is proposed to solve the problem. 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.
ONSA is with the polynomial time complexity.
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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. 403-410, 2009.
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), 2011.
Jehn-Ruey Jiang and Yung-Liang Lai, “Wireless Broadcasting with Optimized Transmission Efficiency,” Journal of Information Science and Engineering (JISE), 2012.
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), 2012.
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Thanks foryour listening!
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