### Document

```Area Coverage
Sensor Deployment and Target Localization in
Distributed Sensor Networks
Area Coverage
2
Area Coverage

Objective


3
Maximize the coverage for a given number of sensors within
a wireless sensor networks.
Propose a Virtual force algorithm (VFA)
Area Coverage

Virtual Force Algorithm(VFA)
4

Attractive force

Repulsive force
Area Coverage

Virtual Force Algorithm(VFA)

Each sensor behaves as a “source of force” for all other sensors
S2
→
F12
Attractive force
Repulsive force
→
F13
S3
S1
→
F14=0
S4
5
Area Coverage

Virtual Force Algorithm(VFA)



→
Fij: the vector exerted on Si by another sensor Sj
Obstacles and areas of preferential coverage also have forces
acting on Si
→
 FiA : the total (attractive) force on Si due to preferential
coverage areas
→
 FiR : the total (repulsive) force on Si due to obstacles
→
The total force Fi on Si
Fi 
6
k
F
j 1, j i
ij
 FiA  FiR
Area Coverage

Virtual Force Algorithm(VFA)


7
Uses a force-directed approach to improve the coverage after
initial random deployment
 Negligible computation time
 Flexibility
Area Coverage
Movement-Assisted Sensor Deployment
Area Coverage

Motivation
sensor
sensing
range
9
Area Coverage

Deploying more static sensors cannot solve the
problem due to wind or obstacles
10
Area Coverage

General idea:
Detecting
coverage hole
11
Move to heal
the hole
Area Coverage

Coverage Hole Detection
Only check local Voronoi cell
sensing range
12
Area Coverage
Coverage hole
exists?
13
Calculate the target
location
(by VEC, VOR or Minimax)
Area Coverage

The VECtor-Based Algorithm (VEC)

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Motivated by the attributes of electrical particles
Virtual force pushes sensors away from dense area
A
B
C
14
A
B
C
Area Coverage

The VORonoi-Based Algorithm (VOR)


Move towards the farthest Voronoi vertex
Avoid moving oscillation: stop for one round if move
backwards
M
B
15
M
B
Area Coverage

The Minimax Algorithm

Move to where the distance to the farthest voronoi vertex is
minimized
M
M
B
B
N
16
N
Target Coverage
Energy-Efficient Target Coverage in Wireless
Sensor Networks
Target Coverage
Sleep
Active
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Area coverage problem
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Sensing overall area
Minimizing active nodes
Target Coverage
Sleep
Active
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Target coverage problem
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19
Sensing all targets
Minimizing active nodes
Target
Target Coverage
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Disjoint Set Covers
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
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
Divide sensor nodes into disjoint sets
Each set completely monitor all targets
One set is active each time until run out of energy
Goal: To find the maximum number of disjoint sets
This is NP-Complete
Disjoint set cover same
time interval
20
Non-disjoint set cover
different time interval
Target Coverage
Sensor
s1
s2
s3
s4
Target
r1
r2
r3
All sensors are active
21
s1
r1
s3
s4
r3
r2
s2
Target Coverage
Sensor
s1
s2
s3
s4
Disjoint sets
S1 = {s1, s2}
S2 = {s3, s4}
22
Target
r1
r2
r3
s1
r1
s3
s4
r3
r2
s2
Target Coverage
t2 t3 t4
t1
s1
s2
s3
s4
r1
r2
r3
r1
s3
Another Approach:
S1 = {s1, s2} with t1 = 0.5
S2 = {s2, s3} with t2 = 0.5
S3 = {s1, s3} with t3 = 0.5
S4 = {s4} with t4 = 1
s1
s4
r3
r2
s2
Target Coverage
s1
r1
s2
r2
s3
r3
s4
r1
s3
s4
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Minimum Set
element
S1
s1 , s2
S2
s1 , s3
S3
s2 , s3
S4
s4
s1
r3
r2
s2
Target Coverage


Set active interval = 0.5
choose a available set
S1
S2
S3
Minimum Set
element
S1
s1 , s2
S2
s1 , s3
S3
s2 , s3
S4
s4
S4
S4
remainder
life time
remainder
life time
remainder
life time
remainder
life time
remainder
life time
remainder
life time
s1
1
0.5
0
0
0
0
s2
1
0.5
0.5
0
0
0
s3
1
1
0.5
0
0
0
s4
1
1
1
1
0.5
0

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This order is not unique, tried all the orders and
pick up the order with the maximum life time
Target Coverage

Maximum Set Covers (MSC) Problem


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Given:
 C : set of sensors
 R : set of targets
Goal:
 Determine a number of set covers S1, …, Sp and t1,…, tp
 where:
 Si completely covers R
 Maximize t1 + … + tp
 Each sensor is not active more than 1
MSC is NP-Complete
Target Coverage


Using Linear Programming Approach
Given:



A set of n sensor nodes: C = {s1, s2, …, sn}
A set of m targets: R={r1, r2, …, rm}
The relationship between sensors and targets:
Ck = {i|sensor si covers target rk}
s1
s2
s3

r1
r2
r3
C = {s1, s2, s3};
R = {r1, r2, r3}
C1 = {1, 3}; C2 = {1, 2}; C3 = {2, 3}
Variables:


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xij = 1 if si ∈ Sj, otherwise xij = 0
tj ∈[0, 1], represents the time allocated for Sj
Target Coverage
Maxim ize t1  ...  t p
p
subject to
x t
ij j
j 1
x
iC k
ij
 1 si  C
 1 rk  R, j  1,.., p
where xij  0,1 ( xij  1 iff si  S j )
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all targets must be covered
Barrier Coverage
Strong Barrier Coverage of Wireless Sensor
Networks
Barrier Coverage
USA
MEXICO
33
Barrier Coverage

How to define a belt region?

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Parallel curves
Region between two parallel curves
Barrier Coverage
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Two special belt region
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Rectangular:
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Donut-shaped:
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Barrier Coverage
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Crossing paths
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A crossing path is a path that crosses the complete width of
the belt region.
Crossing paths
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Not crossing paths
Barrier Coverage
Weak barrier coverage
Strong barrier coverage
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Barrier Coverage

k-covered
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A crossing path is said to be k-covered if it intersects the
sensing disks of at least k sensors.
3-covered
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1-covered
0-covered
Barrier Coverage

k-barrier covered
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A belt region is k-barrier covered if all crossing paths are kcovered.
Not barrier coverage
1-barrier coverage
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Barrier Coverage
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Reduced to k-connectivity problem

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Given a sensor network over a belt region
Construct a coverage graph G(V, E)

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V: sensor nodes, plus two dummy nodes L, R
E: edge (u,v) if their sensing disks overlap
Region is k-barrier covered if L and R are k-connected in G.
L
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R
Barrier Coverage
3-barrier
3-barrier
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Barrier Coverage
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Characteristics
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
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Improved robustness of the barrier coverage
Lower communication overhead and computation costs
Strengthened local barrier coverage
failure
without vertical strip
42
failure
with vertical strip
Surface Coverage in Wireless Sensor
Networks
IEEE INFOCOM 2009
Ming-Chen Zhao, Jiayin Lei, Min-You Wu, Yunhuai Liu,
Wei Shu
Shanghai Jiao Tong Univ., Shanghai
43
Motivation

Existing studies on Wireless Sensor Networks (WSNs)
focus on 2D ideal plane coverage and 3D full space
coverage.

The 3D surface of a targeted Field of Interest is complex
in many real world applications.

Existing studies on coverage do not produce practical
results.
44
Motivation

In surface coverage, the targeted Field of Interest is a
complex surface in 3D space and sensors can be
deployed only on the surface.

Existing 2D plane coverage is merely a special case of
surface coverage.

Simulations point out that existing sensor deployment
schemes for a 2D plane cannot be directly applied to
surface coverage cases.
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Introduction

volcano monitoring
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Introduction

Surface Coverage
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47
use triangularization to partition a surface
Models
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Sensor models
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sensing radius r in 3D Euclid space
statically deployed
Surface models

z = f(x, y)

z=
48
c,
ax + by + c,
if the surface is a plane
if the surface is a slant
Problem Statement

Problems in WSN surface coverage:
 1. The number of sensors that are needed to reach a
certain expected coverage ratio under stochastic
deployment.
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Problem Statement

Problems in WSN surface coverage:
 2. The optimal deployment strategy with guaranteed full
coverage and the least number of sensors when
sensor deployment is pre-determined.
50
Optimum Partition Coverage
Problem (OPCP)

Convert optimum surface coverage problem to a discrete
problem and then relate those results back to the original
continuous problem.
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Optimum Partition Coverage
Problem (OPCP)
S: P = {SA, SB, SC, SD, SE, SF}

h*(Lα)=h(1)∪h(3)∪h(4)∪h(5)
1
6
A
B
F
5
Lα = {1, 3, 4, 5}
2
C
7
E
D
4
|Lα| = 4
3
Lβ = {3, 6, 7}
|Lβ| = 3
53
minimum
Optimum Partition Coverage
Problem (OPCP)

Algorithm 1: Greedy algorithm
1
6
A
B
F
5
C
7
E
D
4
54
2
3
Optimum Partition Coverage
Problem (OPCP)

Greedy algorithm

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Time complexity


55
selects a position that can increase the covered region the
most
O(|P|2)
log (|P|) approximation algorithm
Trap Coverage
56
Motivation

Tracking of movements such as that of people,
animals, vehicles, or of phenomena such as ﬁre can be
achieved by deploying a wireless sensor network.

Real-life deployments, will be at large scale and
achieving this scale will become prohibitively
expensive if we require every point in the region to
be covered (i.e., full coverage), as has been the case in
prototype deployments.
57
Motivation

Trap Coverage scales well with large deployment
regions.

A sensor network providing Trap Coverage
guarantees any moving object can move at most a
displacement before it is guaranteed to be detected
by the network.

Trap Coverage generalizes the real model of full
coverage by allowing holes of a given maximum
diameter.
58
Trap Coverage: Allowing Coverage
Holes of Bounded Diameter in
Wireless Sensor Networks
Paul Balister, Santosh Kumar, Zizhan
Zheng, and Prasun Sinha IEEE INFOCOM 2009
59
Introduction

Real-life deployments, will be at large scale and
achieving this scale will become prohibitively
expensive if we require every point in the region to
be covered (i.e., full coverage), as has been the case in
prototype deployments.
60
Introduction

Trap Coverage

Guarantees that any moving object or phenomena can move
at most a (known) displacement before it is guaranteed to
be detected by the network.
Hole Diameter
61
Introduction

Trap Coverage


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d is the diameter of the largest hole
Full Coverage: d is set to 0
Introduction

Define a Coverage Hole in a target region of deployment
A to be a connected component1 of the set of uncovered
points of A.

Trap Coverage with diameter d to A if the diameter of
any Coverage Hole in A is at most d.
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Estimating the Density for Random
Deployments

Example of Poisson deployment
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holes of larger diameters are typically long and thin
Computing the Trap Coverage
Diameter



Discovering Hole Boundary
Diameter Computation
Coping with Sensing Region Uncertainty
65
Computing the Trap Coverage
Diameter

Discovering Hole Boundary

Boundary node
S1
S2
Boundary
node
66
Computing the Trap Coverage
Diameter

Discovering Hole Boundary

Hole Boundary: hole loop–outermost curves
diamH
67
Computing the Trap Coverage
Diameter

Diameter Computation

Crossing: intersection point of perimeters
diamXH
68
Computing the Trap Coverage
Diameter

Diameter Computation

Crossing: intersection point of perimeters
diamXH +2D
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Computing the Trap Coverage
Diameter

Diameter Computation




H : denote a hole loop
XH : denote the set of crossings on the loop
 Crossing: an intersection point of either two sensing
perimeters
D : the maximum diameter of all sensing regions
Lemma 5.1: diamXH ≤ diamH ≤ diamXH +2D
70
Evaluation and Deployment in
Wireless Sensor Networks


71
This paper, considers two sub-problems: k-coverage
contour evaluation and k-coverage rate deployment.
The former aims to evaluate the coverage level of any
location inside a monitored area, while the latter aims
to determine the locations of a given set of sensors
to guarantee the maximum increment of k-coverage
rate when they are deployed into the area.
k-Fully covered and k-partially
covered




An area A’ is called to be fully covered by a sensor s if
each point in A’ is covered by s.
A’ is called to be partially covered by s if some points in
A’ are covered by s and some are not.
If A’ is not fully covered or partially covered by any
sensor, then A’ is uncovered.
For simplicity, an area fully covered by exactly k distinct
sensors is called to be exactly k-fully and an area partially
covered by exactly k distinct sensors is called to be
exactly k-partially covered.
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g4
g2
s2
g3
g1
g5
s3
s1
Zero-Partially Covered
Non-Zero Partially Covered
An example of fully covered, partially covered, and
uncovered grids. Each grid has side length r/2.
73
k-COVERAGE CONTOUR
EVALUATION SCHEME (K-CCE)



When a grid g is partially covered by s, evaluating
what percentage of g is covered by s requires
complex computation.
The matter goes worse as grids are partially covered
by more than one sensor.
Instead of applying complex computation, we can
divide the grid into sub-grids to obtain more precise
coverage information.
74
s2
a b
c d
Zero - Partially Covered Grid
s3
s1
2-Fully Covered Grid
Uncertain Grid
An example of each grid with side length r/4.
75
K-CCE

Besides, for k-coverage contour evaluation, grids
which are fully covered by at least k sensors do not
need any more division. Hence, division shall be
performed on those grids which are partially covered
by at least one sensor and fully covered by less than k
distinct sensors.
76
s2
Zero - Partially Covered Grid
s3
s1
2-Fully Covered Grid
Uncertain Grid
An example of non-uniform-sized grids.
77
Maximum Tolerable Evaluation Error
(MTEE)

Maximum Evaluation Error (MEE) is the ratio of
uncertainly covered area relative to whole monitored
area, i.e., MEE = ∑g  U |g|/|A|, where U denotes the set of
uncertain grids, and |g| and |A| denote the area size of g
and A, respectively.

Maximum Tolerable Evaluation Error (MTEE) is the
maximum evaluation error that is permitted for a target
application.
78
An example of grid division.
79
k-COVERAGE RATE DEPLOYMENT
SCHEME (K-CRD)


The basic idea of this scheme is to deploy sensors to
locations that increase the total area of k-fully covered
grids most economically
Given a grid g, we define a deployment region with
respect to g, denoted by DR(g), as an area within which a
sensor is deployed can fully cover g.
80
The original deployment region
with respect to grid g.
The dashed circle is a simplified
deployment region with respect to
grid g.
81
Two Heuristics



We employ the following two heuristics to deploy the
sensors economically (in terms of the number of sensors
used).
First, consider λ = {max i | there exists some grid g that is
i-fully covered and i < k}. It is clear that deploying sensors
to fully cover the λ-fully covered grids improves the kcoverage rate
Second, define a candidate grid to be a λ -fully covered
grid. Among all candidate grids, deploying sensors to fully
cover the ones with the largest area is an even more
economic way.
82
Intersection of deployment regions. (a) Intersection of DR(g1)
and DR(g2); (b) Points Pb Pc, and Pe are best_fits.
83
k-CRD1


Define grid-weight of grid g, GW(g), to be |g| if g is a
candidate grid and 0 otherwise.
The main idea is based on the observation that there
is a high possibility that a best_fit is a fit with respect
to a higher-grid-weight grid.
84
The first three candidate grids are at left-up, right-up,
and left-down corner.
85
k-CRD1


Clearly, fits with respect to grids at left-up, right-up,
and left-down corner are in I1, I2, and I3, respectively.
Besides, fit with respect to the grid at left-down
corner has the highest weight. So, we deploy a sensor
in fit with respect to grid at left-down corner.
86
k-CRD2



In order to further reduce the computation cost, the
main motivation of scheme k-CRD2 is to avoid high
computation cost of determining fits.
In k-CRD2, only highest-grid-weight candidate grids
are considered.
Let C1 denote the set of highest-grid-weight
candidate grids. Randomly choose a candidate grid g
from C1. Deploy k sensors at a point p satisfying that


87
(1) p is located in DR(g); and
(2) maximal number of grids in C1 can be fully covered.
Randomly choose a grid from
C1, say g6. Then deploy (4-3)
sensor at point u because
maximum number of grids
(i.e., g5 and g6) in C1 can be
fully covered.
88
An example of 4-CRD2. C1={g1,
g2, … , g8 }.
```