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Chapter 14 (part I)

WSN: Coverage and Energy Conservation

國立交通大學 資訊工程系曾煜棋教授

Prof. Yu-Chee Tseng

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Research Issues in Sensor Networks Hardware (2000)

CPU, memory, sensors, etc. Protocols (2002)

MAC layers Routing and transport protocols

Applications (2004) Localization and positioning applications

Management (2008) Coverage and connectivity problemsCoverage and connectivity problems Power managementPower management etc.etc.

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Coverage Problems In general

Determine how well the sensing field is monitored or tracked by sensors.

Possible Approaches Geometric Problems Level of Exposure Area Coverage

Coverage Coverage and Connectivity Coverage-Preserving and Energy-Conserving Problem

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Review: Art Gallery Problem Place the minimum number of cameras

such that every point in the art gallery is monitored by at least one camera.

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Review: Circle Covering Problem Given a fixed number of identical circles,

the goal is to minimize the radius of circles.

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Level of Exposure Breach and support paths

paths on which the distance from any point to the closest sensor is maximized and minimized

Voronoi diagram and Delaunay triangulation Exposure paths

Consider the duration that an object is monitored by sensors

I

F

I

F

I

F

s

1

2

3

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Coverage and Connectivity Extending the coverage such that

connectivity is maintained. A region is k-covered, then the sensor network

is k-connected if RC 2RS

Query Region

Region covered by selected nodes

C5

C7

C6

C1

C2 C3

C4

C5

C6

C7

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Coverage-Preserving and Energy-Conserving Protocols Sensors' on-duty time should be properly

scheduled to conserve energy. This can be done if some nodes share the common

sensing region. Question: Which sensors below can be turned off?

a b

c d

a b

c d

e

f

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The Coverage Problems in 2D

Spaces

(ACM MONET, 2005)

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Coverage Problems In general

To determine how well the sensing field is monitored or tracked by sensors

Sensors may be randomly deployed

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Coverage Problems We formulate this problem as

Determine whether every point in the service area of the sensor network is covered by at least sensors

This is called “sensor –coverage problem”. Why sensors?

Fault tolerance, quality of service applications: localization, object tracking, video

surveillance

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The 2D Coverage ProblemSo this area

is not 1-covered!

1-covered means

that every point in

this area is covered by at least 1 sensor

2-covered means

that every point in

this area is covered by at least 2 sensors

This region is not covered by

any sensor!

Is this area 1-

covered?

This area is not only 1-covered,

but also 2-covered!

What is the coverage

level of this area?

Coverage level = means that this area

is -covered

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Sensing and Communication Ranges

1Honghai Zhang and Jennifer C. Hou, ``On deriving the upper bound of -lifetime for large sensor networks,'' Proc. ACM Mobihoc 2004, June 2004

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Assumptions Each sensor is aware of its geographic

location and sensing radius. Each sensor can communicate with its

neighbors.

Difficulties: There are an infinite number of points in any

small field. A better way: O(n2) regions can be divided by n

circles How to determine all these regions?

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The Proposed Solution

We try to look at how the perimeterperimeter of each sensor’s sensing range is covered. How a perimeter is covered implies how an area is

covered … by the continuity of coverage of a region

By collecting perimeter coverageperimeter coverage of each sensor, the level of coverage of an areacoverage of an area can be determined. a distributed solution

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0 j1,L

j2,L

j1,R

j2,R

si

j1,R

j1,L

j2,R

j2,L

0

j 1 ,L j 3 ,L

j 2 ,L

j 1 ,R j 3 ,R

j 2 ,R

s i

j 3 ,L

j 3 ,R

j 1 ,R

j 1 ,L

j 2 ,R

j 2 ,L

0 j1,L j1,R

si

j1,R

j1,L

0

r r

s i

s j

How to calculate the perimeter cover of a sensor?

Si is 2-perimeter-

covered

0 j1,L j3,L

j2,L j4,L j6,L

j5,L

j7,L j8,L

j1,R j3,R

j2,R j4,Rj6,R

j5,R

j7,Rj8,R

j8,L

j8,R

si

j3,L

j4,L

j7,L

j6,L

j5,L

j3,R

j4,R

j7,R

j6,R

j5,R

j1,R

j1,L

j2,R

j2,L

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Relationship between k-covered and k-perimeter-covered

THEOREM. Suppose that no two sensors are located in the same location. The whole network area A is k-coveredk-covered iff each sensor in the network is k-perimeter-coveredk-perimeter-covered.

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Detailed Algorithm Each sensor independently calculates its

perimeter-covered. k = min{each sensor’s perimeter coverage}

Time complexity: nd log(d) n: number of sensors d: number of neighbors of a sensor

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Simulation Results

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A Toolkit

(a) (b)

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Summary An important multi-level coverage

problem! We have proposed efficient polynomial-

time solutions. Simulation results and a toolkit based on

proposed solutions are presented.

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The Coverage Problem in 3D

Spaces

(IEEE Globecom 2004)

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The 3D Coverage ProblemWhat is the

coverage level of this 3D

area?

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The 3D Coverage Problem Problem Definition

Given a set of sensors in a 3D sensing field, is every point in this field covered by at least sensors?

Assumptions: Each sensor is aware of its own location as well

as its neighbors’ locations. The sensing range of each sensor is modeled by

a 3D ball. The sensing ranges of sensors can be non-

uniform.

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Overview of Our Solution The Proposed Solution

We reduce the geometric problem from a 3D space to one in a 2D space, and then from a 2D space to one in a 1D space.

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Reduction Technique (I) 3D => 2D

To determine whether the whole sensing field is sufficiently covered, we look at the spheres of all sensors

Theorem 1: If each sphere is -sphere-covered, then the sensing field is -covered. Sensor si is-sphere-covered if all points on its

sphere are sphere-covered by at least sensors, i.e., on or within the spheres of at least sensors.

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Reduction Technique (II) 2D => 1D

To determine whether each sensor’s sphere is sufficiently covered, we look at how each spherical cap and how each circle of the intersection of two spheres is covered. (refer to the next page)

Corollary 1: Consider any sensor si. If each point on Si is -cap-covered, then sphere Si is -sphere-covered. A point p is -cap-covered if it is on at least caps.

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Cap and Circle

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k-cap-covered p is 2-cap-covered (by Cap(i, j) and Cap(i,

k)).

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Reduction Technique (III) 2D => 1D

Theorem 2: Consider any sensor si and each of its neighboring sensor sj. If each circle Cir(i, j) is -circle-covered, then the sphere Si is -cap-covered.

A circle is -circle-covered if every point on this circle is covered by at least caps.

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k-circle-covered Cir(i, j) is 1-circle-covered (by Cap(i, k)).

Cir(i, j)

Cap(i, k)

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Reduction Technique (IV) 2D => 1D

By stretching each circle on a 1D line, the level of circle coverage can be easily determined.

This can be done by our 2-D coverage solution.

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Reduction Example

=>

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Reduction Example

=>

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Calculating the Circle Coverage

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Calculating the Circle Coverage

=>

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Calculating the Circle Coverage

=>

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Calculating the Circle Coverage

=>

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The Complete Algorithm Each sensor si independently calculates

the circle coverage of each of the circle on its sphere. sphere coverage of si =

min{ circle coverage of all circles on Si }

overall coverage = min{ sphere coverage of all sensors }

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Complexity To calculate the sphere coverage of one

sensor: O(d2logd) d is the maximum number of neighbors of a

sensor Overall: O(nd2logd)

n is the number of sensors in this field

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Short Summary We define the coverage problem in a 3D

space. Proposed solution

3D => 2D => 1D Network Coverage => Sphere Coverage =>

Circle Coverage Applications

Deploying sensors Reducing on-duty time of sensors

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A Decentralized Energy-Conserving, Coverage-Preserving Protocol

(IEEE ISCAS 2005)

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Overview Goal: prolong the network lifetime Schedule sensors’ on-duty time

Put as many sensors into sleeping mode as possible

Meanwhile active nodes should maintain sufficient coverage

Two protocols are proposed: basic scheme (by Yan, He, and Stankovic, in

ACM SenSys 2003) energy-based scheme (by Tseng, IEEE ISCAS

2005)

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Basic Scheme Two phases

Initialization phase: Message exchange Calculate each sensor’s working scheduleworking schedule in the next

phase Sensing phase:

This phase is divided into multiple rounds. In each round, a sensor has its own working scheduleworking schedule..

Reference time:Reference time: Each sensor will randomly generate a number in the Each sensor will randomly generate a number in the

range [0, cycle_length] as its reference time. range [0, cycle_length] as its reference time.

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Structure of Sensors’ Working Cycles Theorem:

If each intersection point between any two sensors’ boundaries is always covered, then the whole sensing field is always covered.

Basic Idea: Each sensor i and its neighbors will share the

responsibility, in a time division manner, to cover each intersection point.

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a

b c

d

An Example (to calculate sensor a’s working schedule)

Sensing phaseInitial phase

Round 1 Round 2 ……… Round n

Initial phase

聯集 : a’s final on-duty time in round i

Round i

Ref a Ref b Ref cRef d

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more details … The above will also be done by sensors b,

c, and d. This will guarantee that all intersection

points of sensors’ boundaries will be covered over the time domain.

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Energy-Based Scheme goal: based on remaining energy of sensors

Nodes with more remaining energies should work longer. Each round is logically separated into two zones:

larger zone: 3T/4 smaller zone: T/4.

Reference time selection: If a node’s remaining energy is larger than ½ of its

neighbors‘, randomly choose a reference time in the larger zone.

Otherwise, choose a reference time in the smaller zone. Work schedule selection:

based on energy (refer to the next page)

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Energy-Based Scheme (cont.) Frontp,i and Backp,i are also selected based

on remaining energies.

', [( ( ))mod ] i

p i i i rndi i

EFront Ref prev Ref T

E E

'', [( ( ) )mod ] i

p i i i rndi i

EBack next Ref Ref T

E E

Round i

Ref a Ref b Ref cRef d

richer

richpoor

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Two Enhancements k-Coverage-Preserving Protocol

(omitted)

active time optimization Longest Schedule First (LSF) Shortest Lifetime First (SLF)

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Simulation Results

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Simulation Results (cont.)

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Summary A distributed node-scheduling protocol

Conserve energy Preserve coverage Handle k-coverage problem

Advantage Distribute energy consumption among nodes

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Conclusions a survey of solutions to the coverage

problems Both in 2D and 3D spaces

a survey of solutions to coverage-preserving, energy-conserving problems Fairly distribute sensors’ energy expenditure

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References1. C.-F. Huang and Y.-C. Tseng, “The Coverage Problem in a

Wireless Sensor Network”, ACM Mobile Networking and Applications (MONET), Special Issue on Wireless Sensor Networks.

2. C.-F. Huang and Y.-C. Tseng, “A Survey of Solutions to the Coverage Problems in Wireless Sensor Networks”, Journal of Internet Technology, Special Issue on Wireless Ad Hoc and Sensor Networks.

3. C.-F. Huang and Y.-C. Tseng, “The Coverage Problem in a Wireless Sensor Network”, ACM Int’l Workshop on Wireless Sensor Networks and Applications (WSNA) (in conjunction with ACM MobiCom), 2003.

4. C.-F. Huang, Y.-C. Tseng, and Li-Chu Lo, “The Coverage Problem in Three-Dimensional Wireless Sensor Networks”, IEEE GLOBECOM, 2004.

5. C.-F. Huang, L.-C. Lo, Y.-C. Tseng, and W.-T. Chen, “Decentralized Energy-Conserving and Coverage-Preserving Protocols for Wireless Sensor Networks”, Int’l Symp. on Circuits and Systems (ISCAS), 2005.