sink-connected barrier coverage optimization for wireless sensor networks

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

4

WSN: Wireless Sensor Network

Sensing Range

Communication Range

Sensor Node

SinkNode

5

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


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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


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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


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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


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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



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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 N6 N7 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

30

Outline



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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 N6 N7 N8

N3 N4

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=0X

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 o

f Sel

ecte

d N

odes

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


Num

ber o

f Sel

ecte

d N

odes

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

200400600800

100012001400160018002000

ONSA (1 source)GDA (1 source)ONSA (2 sources)GDA (2 sources)


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)


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

50

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

51

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!

sink-connected barrier coverage optimization for wireless sensor networks

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