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國立交通大學 資訊工程系 曾煜棋 教授
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Wireless Sensor Networks: Coverage and Energy Conservation Issues
國立交通大學 資訊工程系
曾煜棋教授 Prof. Yu-Chee Tseng
國立交通大學 資訊工程系 曾煜棋 教授
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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 problems Power management etc.
國立交通大學 資訊工程系 曾煜棋 教授
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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
國立交通大學 資訊工程系 曾煜棋 教授
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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.
國立交通大學 資訊工程系 曾煜棋 教授
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Review: Circle Covering Problem Given a fixed number of identical circles,
the goal is to minimize the radius of circles.
國立交通大學 資訊工程系 曾煜棋 教授
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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
國立交通大學 資訊工程系 曾煜棋 教授
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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
國立交通大學 資訊工程系 曾煜棋 教授
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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
國立交通大學 資訊工程系 曾煜棋 教授
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The Coverage Problems in 2D Spaces (ACM MONET, 2005)
國立交通大學 資訊工程系 曾煜棋 教授
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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
國立交通大學 資訊工程系 曾煜棋 教授
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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 α sensors
This is called “sensor α–coverage problem”. Why α sensors?
Fault tolerance, quality of service applications: localization, object tracking, video
surveillance
國立交通大學 資訊工程系 曾煜棋 教授
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The 2D Coverage Problem So 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 = α means that this area
is α-covered
國立交通大學 資訊工程系 曾煜棋 教授
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Sensing and Communication Ranges
1Honghai Zhang and Jennifer C. Hou, ``On deriving the upper bound of α-lifetime for large sensor networks,'' Proc. ACM Mobihoc 2004, June 2004
國立交通大學 資訊工程系 曾煜棋 教授
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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?
國立交通大學 資訊工程系 曾煜棋 教授
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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
國立交通大學 資訊工程系 曾煜棋 教授
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0 2π
αj1,L
αj2,L
αj1,R
αj2,R
si
αj1,R
αj1,L
αj2,R
αj2,L
0 2π
α j1,L α j3,L
α j2,L
α j1,R α j3,R
α j2,R
s i
α j3,L
α j3,R
α j1,R
α j1,L
α j2,R
α j2,L
0 2π
αj1,L αj1,R
si
αj1,R
αj1,L
0 2ππ−α π+α
r r
αs i
s j α
How to calculate the perimeter cover of a sensor?
Si is 2-perimeter-
covered
0 2π
αj1,L αj3,L
αj2,L αj4,L αj6,L
αj5,L
αj7,L αj8,L
αj1,R αj3,R
αj2,R αj4,Rαj6,R
αj5,R
αj7,Rαj8,R
αj8,L
αj8,R
si
αj3,L
αj4,L
αj7,L
αj6,L
αj5,L
αj3,R
αj4,R
αj7,R
αj6,R
αj5,R
αj1,R
αj1,L
αj2,R
αj2,L
國立交通大學 資訊工程系 曾煜棋 教授
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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-covered iff each sensor in the network is k-perimeter-covered.
國立交通大學 資訊工程系 曾煜棋 教授
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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
國立交通大學 資訊工程系 曾煜棋 教授
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Simulation Results
國立交通大學 資訊工程系 曾煜棋 教授
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A Toolkit
(a) (b)
國立交通大學 資訊工程系 曾煜棋 教授
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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.
國立交通大學 資訊工程系 曾煜棋 教授
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The Coverage Problem in 3D Spaces
(IEEE Globecom 2004)
國立交通大學 資訊工程系 曾煜棋 教授
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The 3D Coverage Problem What is the
coverage level of this 3D
area?
國立交通大學 資訊工程系 曾煜棋 教授
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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 α 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.
國立交通大學 資訊工程系 曾煜棋 教授
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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.
國立交通大學 資訊工程系 曾煜棋 教授
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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 α-sphere-covered, then the sensing field is α-covered. Sensor si is α-sphere-covered if all points on its
sphere are sphere-covered by at least α sensors, i.e., on or within the spheres of at least α sensors.
國立交通大學 資訊工程系 曾煜棋 教授
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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 α-cap-covered, then sphere Si is α-sphere-covered. A point p is α-cap-covered if it is on at least α caps.
國立交通大學 資訊工程系 曾煜棋 教授
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Cap and Circle
國立交通大學 資訊工程系 曾煜棋 教授
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k-cap-covered p is 2-cap-covered (by Cap(i, j) and Cap(i,
k)).
國立交通大學 資訊工程系 曾煜棋 教授
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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 α-circle-covered, then the sphere Si is α-cap-covered.
A circle is α-circle-covered if every point on this circle is covered by at least α caps.
國立交通大學 資訊工程系 曾煜棋 教授
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k-circle-covered Cir(i, j) is 1-circle-covered (by Cap(i, k)).
Cir(i, j)
Cap(i, k)
國立交通大學 資訊工程系 曾煜棋 教授
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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.
國立交通大學 資訊工程系 曾煜棋 教授
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Reduction Example
=>
國立交通大學 資訊工程系 曾煜棋 教授
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Reduction Example
=>
國立交通大學 資訊工程系 曾煜棋 教授
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Calculating the Circle Coverage
國立交通大學 資訊工程系 曾煜棋 教授
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Calculating the Circle Coverage
=>
國立交通大學 資訊工程系 曾煜棋 教授
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Calculating the Circle Coverage
=>
國立交通大學 資訊工程系 曾煜棋 教授
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Calculating the Circle Coverage
=>
國立交通大學 資訊工程系 曾煜棋 教授
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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 }
國立交通大學 資訊工程系 曾煜棋 教授
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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
國立交通大學 資訊工程系 曾煜棋 教授
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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
國立交通大學 資訊工程系 曾煜棋 教授
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A Decentralized Energy-Conserving, Coverage-Preserving Protocol
(IEEE ISCAS 2005)
國立交通大學 資訊工程系 曾煜棋 教授
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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)
國立交通大學 資訊工程系 曾煜棋 教授
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Basic Scheme Two phases
Initialization phase: Message exchange Calculate each sensor’s working schedule in the next
phase
Sensing 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.
國立交通大學 資訊工程系 曾煜棋 教授
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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.
國立交通大學 資訊工程系 曾煜棋 教授
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a
b c
d
An Example (to calculate sensor a’s working schedule)
Sensing phase Initial 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 c Ref d
國立交通大學 資訊工程系 曾煜棋 教授
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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.
國立交通大學 資訊工程系 曾煜棋 教授
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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)
國立交通大學 資訊工程系 曾煜棋 教授
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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 c Ref d
richer
rich poor
國立交通大學 資訊工程系 曾煜棋 教授
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Two Enhancements k-Coverage-Preserving Protocol
(omitted)
active time optimization
Longest Schedule First (LSF) Shortest Lifetime First (SLF)
國立交通大學 資訊工程系 曾煜棋 教授
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Simulation Results
國立交通大學 資訊工程系 曾煜棋 教授
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Simulation Results (cont.)
國立交通大學 資訊工程系 曾煜棋 教授
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Summary A distributed node-scheduling protocol
Conserve energy Preserve coverage Handle k-coverage problem
Advantage Distribute energy consumption among nodes
國立交通大學 資訊工程系 曾煜棋 教授
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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
國立交通大學 資訊工程系 曾煜棋 教授
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References 1. 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.