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
1
Research Issues in Sensor Networks

Hardware (2000)


Protocols (2002)



MAC layers
Routing and transport protocols
Applications (2004)


CPU, memory, sensors, etc.
Localization and positioning applications
Management (2008)



Coverage and connectivity problems
Power management
etc.
2
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
3
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.
4
Review: Circle Covering Problem

Given a fixed number of identical circles,
the goal is to minimize the radius of circles.
5
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
1
2
I
I
F
s
F
3
F
6
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
Region covered
by selected nodes
Query Region
C1
C2
C3
C4
C5
C5
C6
C7
C6
C7
7
Coverage-Preserving and EnergyConserving 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
a
b
d
c
d
e
f
c
8
The Coverage Problems
in 2D Spaces
(ACM MONET, 2005)
9
Coverage Problems

In general


To determine how well the sensing field is
monitored or tracked by sensors
Sensors may be randomly deployed
10
Coverage Problems

We formulate this problem as



Determine whether every point in the service
area of the sensor network is covered by at
least a sensors
This is called “sensor a–coverage problem”.
Why a sensors?


Fault tolerance, quality of service
applications: localization, object tracking, video
surveillance
11
The 2D
This
area
This
region
What
is
theisisnot
So
this
area
is
Is
this
only
1-covered,
not
covered
by
coverage
not
1-covered!
area
1Coverage
Problem
but
also
2-covered!
any
sensor!
level
of
this
covered?
area?
1-covered
2-covered
means
means
that every
Coverage
level
=a
that
every
in
meanspoint
that
this
area
point in
area
isthis
a-covered
this area
is covered
covered
by at is
least
by at least
1 sensor
2 sensors
12
Sensing and Communication Ranges
Zhang and Jennifer C. Hou, ``On deriving the upper bound of a-lifetime for
large sensor networks,'' Proc. ACM Mobihoc 2004, June 2004
1Honghai
13
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?
14
The Proposed Solution

We try to look at how the perimeter 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 coverage of each sensor,
the level of coverage of an area can be
determined.

a distributed solution
15
How to calculate the perimeter cover of
a sensor?
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16
Relationship between k-covered and kperimeter-covered

THEOREM. Suppose that no two sensors are
located in the same location. The whole network
area A is k-covered iff each sensor in the network
is k-perimeter-covered.
17
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
18
Simulation Results
19
A Toolkit
(a)
(b)
20
Summary
An important multi-level coverage problem!
 We have proposed efficient polynomialtime solutions.
 Simulation results and a toolkit based on
proposed solutions are presented.

21
The Coverage Problem in
3D Spaces
(IEEE Globecom 2004)
22
The 3D Coverage
What is the
coverage level
Problem
of this 3D
area?
23
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 a
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 nonuniform.
24
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.
25
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 a-spherecovered, then the sensing field is a-covered.

Sensor si is a-sphere-covered if all points on its
sphere are sphere-covered by at least a sensors, i.e.,
on or within the spheres of at least a sensors.
26
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 a-cap-covered, then sphere Si
is a-sphere-covered.

A point p is a-cap-covered if it is on at least a caps.
27
Cap and Circle
28
k-cap-covered

p is 2-cap-covered (by Cap(i, j) and Cap(i,
k)).
29
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 a-circle-covered, then the sphere Si is acap-covered.
A circle is a-circle-covered if every point on
this circle is covered by at least a caps.
30
k-circle-covered

Cir(i, j) is 1-circle-covered (by Cap(i, k)).
Cap(i, k)
Cir(i, j)
31
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.
32
Reduction Example
=>
33
Reduction Example
=>
34
Calculating the Circle Coverage
35
Calculating the Circle Coverage
=>
36
Calculating the Circle Coverage
=>
37
Calculating the Circle Coverage
=>
38
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 }
39
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
40
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
41
A Decentralized Energy-Conserving,
Coverage-Preserving Protocol
(IEEE ISCAS 2005)
42
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)
43
Basic Scheme

Two phases

Initialization phase:



Sensing phase:



Message exchange
Calculate each sensor’s working schedule in the next
phase
This phase is divided into multiple rounds.
In each round, a sensor has its own working schedule.
Reference time:

Each sensor will randomly generate a number in the
range [0, cycle_length] as its reference time.
44
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.
45
An Example (to calculate sensor a’s
working schedule)
Round 1
………
Round 2
Initial phase
Round n
Sensing phase
Ref a
Ref b
Round i
Ref d
Ref c
Initial phase
c
b
a
d
聯集: a’s final
on-duty time in
round i
46
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.

47
Energy-Based Scheme

goal: based on remaining energy of sensors


Each round is logically separated into two zones:



larger zone: 3T/4
smaller zone: T/4.
Reference time selection:



Nodes with more remaining energies should work longer.
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)
48
Energy-Based Scheme (cont.)

Frontp,i and Backp,i are also selected based
on remaining energies.
Ei
Front p,i [(Ref i  prev(Ref i ))modTrnd ]
Ei  E '
i
Ei
Back p,i [(next(Ref i )  Ref i )modTrnd ]
Ei  E ''
i
richer
poor
Ref a
Ref b
rich
Ref d
Ref c
49
Round i
Two Enhancements

k-Coverage-Preserving Protocol


(omitted)
active time optimization


Longest Schedule First (LSF)
Shortest Lifetime First (SLF)
50
Simulation Results
51
Simulation Results (cont.)
52
Summary

A distributed node-scheduling protocol




Conserve energy
Preserve coverage
Handle k-coverage problem
Advantage

Distribute energy consumption among nodes
53
Conclusions

a survey of solutions to the coverage
problems


Both in 2D and 3D spaces
a survey of solutions to coveragepreserving, energy-conserving problems

Fairly distribute sensors’ energy expenditure
54
References
1.
2.
3.
4.
5.
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.
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.
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.
C.-F. Huang, Y.-C. Tseng, and Li-Chu Lo, “The Coverage Problem
in Three-Dimensional Wireless Sensor Networks”, IEEE
GLOBECOM, 2004.
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.
55