REVIEW OVER HOLE HEALING TECHNIQUES IN WIRELESS SENSOR NETWORKS

International Journal of Ad hoc, Sensor & Ubiquitous Computing (IJASUC) Vol.7, No.1, February 2016
DOI : 10.5121/ijasuc.2016.7101 1
REVIEW OVER HOLE HEALING TECHNIQUES
IN WIRELESS SENSOR NETWORKS
Latesh Mehta and Manik Gupta
Department of Computer Science,
Chitkara University, Himachal Pradesh, India
ABSTRACT
Improving coverage and connectivity is a very important issue in wireless sensor networks. The unattended
or uncovered region in a sensing field is called a coverage hole. A coverage hole impacts the performance
of the wireless sensor network, disconnects the network topology and causes delay in data transmission.
These coverage holes can be healed randomly or each hole can be assigned a priority value for healing. In
this paper we will discuss about various hole healing strategies and their mechanisms.
KEYWORDS
Connectivity, Coverage, Coverage Holes, Hole Healing, Wireless Sensor Network.
1. INTRODUCTION
A wireless sensor consists of a sensing component, on-board processing, communication, and
storage unit. Many sensors cooperatively monitoring a large physical environment, form a
wireless sensor network (WSN)[7]. The wireless sensor networks have different usage in various
fields and applications like monitor and protect civil infrastructure, underwater monitoring[16],
monitor large geographic areas, volcano monitoring, collecting structural health information etc.
In [10] these applications are classified into monitoring and tracking applications e.g. health and
wellness monitoring, power monitoring, inventory location monitoring, tracking objects, animals,
humans, and vehicles. Sometimes, sensors are deployed in very remote and inaccessible areas;
therefore the task of maintaining the coverage and connectivity becomes a major issue in WSN.
The uncovered region in the target sensing field is considered as a coverage hole. Coverage holes
can be introduced as a result of a node failure or initial deployment. Fig.1(a) shows a 2-
dimentional image of a field which shows coverage holes introduced as a result of initial
deployment. Fig. 1(b) shows coverage holes in a field introduced as a result of node failure.
(a) (b)
Figure 1. An example of coverage holes in a target sensing field. (a) 2-dimentional image showing
coverage holes as a result of initial deployment. The white area in the graph shows the uncovered region in
the field.[4] (b) Coverage holes as a result of node failure. Hi represents coverage holes in the field.[6]
Sensor nodes must be self-managing[7] and should discover, identify, and react to network
disruptions. To improve the coverage and maintain the network connectivity various strategies are

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proposed in recent years. In energy-constrained sensor networks, these solutions must be
implemented in such a way that they do not incur excessive energy overheads. In [9] coverage
problem is classified into three categories i.e. area coverage, point coverage and barrier coverage.
In PEAS mechanism[11], based on node density detection, duty cycling is used where some
nodes are allowed to sleep and nodes are awakened at random time interval. In [12] unnecessary
sensing work is avoided by detecting redundant nodes and sending them to a sleep state. The
work in [13] compares energy efficiency of the sensor network with fixed sensing range and the
network consisting of nodes with adjustable sensing range. G-MSC [14], a target coverage
algorithm, constructs continuous node sets to cover as many targets in the network. The coverage
algorithm in [15] relies only on 3 hop neighbors for its information. In[17], holes are classified
into 5 types, namely, coverage hole, routing hole, jamming hole, sink/black hole and worm hole.
The study in[17] also discuss detection of hole using voronoi and triangular diagram approach.
All these studies focuses mainly on the hole detection, but we must not forget after hole detection
the next phase i.e. hole healing is also very important. Healing a coverage hole not only improves
coverage but it also improves the connectivity of the network. The complete hole healing process
can be divided into two parts:Hole Selection and Healing Process.
Figure 2. Classification of Hole Selection and Healing Process.
The hole selection process decides which hole should be selected first for healing and the healing
process tells how the selected hole should be healed to ensure maximum coverage and
connectivity. Fig. 2 shows various types of hole selection methods and healing process. In the rest
of the paper section 2 will give details about various hole selection methods, section 3 will
discuss about healing techniques and section 4 will conclude the paper.
2. HOLE SELECTION METHODS
The hole selection process is very important during the network maintenance process. Coverage
holes in a network are of different shape and size. The effect of their presence in the network is
also different and it depends on various factors such as shape and size of the hole, shape and size
of the target sensing field, location of the hole and the sink etc. Based on these factors some holes
affect the coverage, some affects the connectivity and most of them affect both. The hole which is
disturbing network the most, should be selected for healing at the first place. Based on their effect
on coverage and connectivity, holes should be assigned a priority value for healing. In recent
years, researchers have adopted different methods for hole selection. These methods are as
follows:
Hole Healing
Hole Selection Healing Process
Voronoi Diagram Based
Approach
Random
Weighted Method
Travelling Salesman Problem
Method
Maximum Size
Equally Divided Path
Selection
Delaunay’s Triangulation
Triangular Diagram Based
Approach
Direction Adjustment
Sensor Movement with
Direction Adjustment
Nearest Distance

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2.1. Random
The coverage holes are selected on a random basis. This method increases the coverage but it
does not optimize the results. It is not a good method for hole selection.
2.2. Maximum Size
In this method coverage holes are selected based on the size of the hole. The hole larger in size
will have maximum effect on the coverage of the network. Therefore hole with maximum size is
selected for healing process. This method improves coverage but has better impact on
connectivity than random method.
2.3. Nearest Distance
In a wireless sensor network, nodes communicate with the sink through a multihop network. Each
node passes message coming from other node towards the sink. Fig. 3 shows data flow towards
the sink in a wireless sensor network. Here, nodes closer to the sink will have more data to relay
towards the sink. Hence they are more likely to lose their energy as compared to other nodes in
the network and if the hole occurs near the sink due to node energy depletion it will induce a
delay in data transmission because the messages will have to re-route now to reach the sink.
Therefore, the nearest distance method selects holes closer to the sink for healing, to balance the
traffic load and to reduce the delay in data transmission.
Figure 3. The multi-to-one data flow concept.[6]
2.4. Travelling Salesman Problem
There can be different number of holes at different position of time in a wireless sensor network.
The hole healing strategy always aim to cover all the holes present in the network for a given
interval of time. Therefore, in some hole healing techniques the hole selection procedure is
transformed into travelling salesman problem[4]. If the network is using an external source to
deploy nodes such as mobile robot, unmanned aerial vehicle(UAV) or other kind of resource,
then its path is computed using travelling salesman problem in which a shortest path is computed
where every hole is covered only once starting from an origin and returns to its initial position at
last. Fig. 4(a) shows the center coordinates of coverage holes in a target sensing field and fig. 4(b)
shows the optimal path obtained. This method ensures that every hole is covered once within less
time.
(a) Center Coordinates of hole[4] (b) Optimal Path Trajectory[4]
Figure 4. Hole Selection Procedure converted into Travelling Salesman Problem.[4]
2.5. Weighted Method
This is the most effective hole selection methods available so far. This method not only improves
coverage but it also improves the connectivity. Holes present in the network are given some

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priority for healing and their priority is based on three properties of the coverage hole. These
three properties are as follows[6]:
• Hole Angle Metric: Hole angle tells about the width of the hole. In a wireless sensor
network data is relayed from all sides towards the sink as shown earlier in fig. 3. A wider hole
will hinder data flow towards the sink. The effect on the data transmission is directly proportional
to the width of the hole. Therefore, a hole with greater hole angle will have more effect on data
transmission. Fig. 5 shows how to calculate hole angle. In fig. 5 Hi represents hole, Bj represents
the hole border node, Lj is a ray starting at sink and extends towards Bj. The ray Lj is obtained for
every hole border node Bj and its slope is calculated. The hole border node Bj with maximum
slope is represented by Bu and Bj with minimum slope in represented by Bd. The angle between
these two rays [SINK,Bu) and [Sink,Bd), represented by Θ(Hi) is called the hole angle and it is
calculated as[6]:
Here, [SINK,Hi) represents ray starting at sink and extends towards the center of hole.
Figure 5. Calculation of Hole Angle.[6]
Now, the metric of hole angle is given by[6]:
W(Θ(Hi)) = Θ(Hi) / 180o
;
• Distance Metric: This property is similar to the nearest distance method. As discussed in
nearest distance method, nodes closer to the sink have more data to relay. Hence hole closer to the
sink will have greater influence on the data transmission than the same hole located far away
from the sink. Healing a hole located at a greater distance or located at the edge of the field will
only improve coverage and will have very less effect on the connectivity. Therefore, we can say
that the influence on the data transmission is inversely proportional to the distance of the hole
from the sink. The distance of hole from sink is calculated as[6]:
Where di is the distance of the hole from the sink, Hi.x and Hi.y are the x and y coordinates of the
center of the hole, S0.x and S0.y are the x and y coordinates of the sink. Fig. 6 shows different
holes with their distance from the sink.

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Figure 6. Distance between hole and the sink.[6]
Now the distance metric is given by[6]:
W(len(Hi)) = 1 / di ;
• Depth Metric: If a hole area is very large, it will greatly reduce the coverage ratio and
might result in network topology disconnection. To avoid this, the depth metric is considered. It is
defined as the distance between nearest hole boundary node Bnear and farthest hole boundary node
Bfar, as shown in fig. 7.
Figure 7. Calculation of Depth.[6]
To calculate Bnear and Bfar an angle bisector Lc of the hole angle Θ(Hi) is obtained. This angle
bisector Lc makes contact with the hole at two hole boundary nodes i.e. it passes through the
transmission range of these two nodes. Out of these two nodes, the node near to the sink is called
Bnear and the node far from the sink is called Bfar. The calculation for Bnear, Bfar and the depth
metric W(deep(Hi)) is given as[6]:
Here, Bj represents set of hole boundary nodes, Hi represents the hole, R is the transmission
radius of sensor nodes, d(a,b) gives the distance between a and b.
• These three properties are combined to assign weight to every hole as[6]:
W(Hi) = αW(Θ(Hi)) * βW(len(Hi)) * γW(deep(Hi)) ;
where α, β, γ are positive harmonic coefficients and their value may vary according to the
requirement of the application. These coefficients are defined as: α + β + γ = 1; Hole with
maximum value for weight i.e. W(Hi) will be selected for healing process.
2.6. Comparative Study
The experimental results for Random, Maximum Size, Nearest Distance and Weighted method is
given in fig 8, which shows that weighted method performs better than others in terms of average
delivery hops. Note that in this graph the results are obtained when weighted method is
implemented with equally divided path selection method[6] which will be discussed in section 3
i.e. healing process section. Average Delivery hops is defined as the average number of hops a
message has to go through to reach the sink in a wireless sensor network. A decrease in average

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delivery hops means better connectivity, message will take less time to reach sink and it will also
reduce energy consumption of the network.
Figure 8. Graph for average delivery hops.[6]
The performance of travelling salesman method is evaluated on the basis of coverage rate[4].
Coverage rate means the percentage of area covered when additional nodes are deployed to cover
holes as shown in fig 9. We can see that as we increase the value of additional nodes used for
redeployment, the coverage almost reaches 100%. Here[4], Travelling Salesman method is
implemented with Delaunay’s triangulation method which will be discussed in section 3 i.e.
healing process section.
Figure 9. Graph of increase in coverage rate for Travelling Salesman method implemented with
Delaunay’s triangulation.[4]
The Hole Selection Methods discussed above are compared in table 1 based on their mechanisms
and results.
Table 1. Comparative study for hole selection methods.
Hole Selection
Method
Mechanism Result
Random Hole is selected randomly for healing Does not optimizes results
Maximum Size Hole with maximum size is selected first Improves coverage
Nearest Distance Hole closer to the sink is selected first Improves connectivity
Travelling Salesman
Problem Method
Hole selection is converted into travelling
salesman problem
Covers each and every hole once
within less time.
Weighted Method Hole is selected based on its three
properties i.e. hole angle, distance and
depth.
Improves both connectivity and
coverage.
3. HEALING PROCESS
After hole selection, next step is to carry out the healing process. Healing process should aim to
maximize the coverage as well as maintain the network topology and connectivity. To heal a

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coverage hole, failed nodes are patched or new nodes are redeployed at the location where
coverage is lost. Some healing techniques also aim to maintain the network connectivity by
deploying nodes in such a way that the average delivery hops for the messages travelling in the
network can be reduced. These healing techniques are discussed as follows:
3.1. Voronoi Diagram Based Approach
In wireless sensor networks, voronoi diagram[8][18] is mainly used to detect coverage holes. In
this section we will discuss the healing technique using voronoi diagrams for directional sensor
networks. A voronoi diagram is constructed by the perpendicular bisectors of the line joining
adjacent sensor nodes. These perpendicular bisectors intersect with each other to form a voronoi
cell, see fig 10. The voronoi diagram has some properties:
• One voronoi cell will contain exactly one sensor node.
• Any point inside a voronoi cell will be closer to the sensor node of the given voronoi cell
than any other sensor node in the network, see fig 10, p is a point inside the voronoi cell of sensor
s1 and the distance between p and s1 is shorter than the distance of the point from any other
sensor node.
• For a given set of sensor nodes the voronoi diagram generated will be unique[20].
Figure 10. Voronoi Diagram.[2]
Based on these properties, we can say that, for homogeneous sensor nodes with equal sensing
range, if a point inside a voronoi cell is not covered by the sensor node of the cell than this point
cannot be covered by any other sensor node in the network. Hence, voronoi diagram is also used
to detect coverage holes. In [1][2], the redeployment strategy for homogeneous directional sensor
nodes using voronoi diagram, to improve the coverage ratio is proposed. The sensing model of
directional sensors is shown in fig 11.
Figure 11. Sensing model of directional sensor.[2]
Here, s(xs,ys) is the sensor, Fs(Field of View, FoV) is the area covered by the sensor, α is called
angle of view of the sensor, θ is the working direction of the sensor and it is measured relative to
positive x-axis, r is the sensing radius, ^
w is the unit vector for working direction of the sensor,
p(x,y) is a point covered by the sensor ‘s’. δ is the angle between the vector sp->
and unit vector
^
w.

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Based on this sensing model, to cover the point p(x,y), the sensor s(xs,ys) has to satisfy the
following conditions:
• Distance between ‘p’ and ‘s’ should be less than or equals to ‘r’.
i.e. √( (x-xs)2
+ (y-ys)2
) ≤ r; (1)
• The angle ‘δ’ should be less than or equals to half of ‘α’.
i.e. δ ≤ α/2;
Considering: ‫⃗݌ݏ‬ ⋅ ^
‫ݓ‬ = ||‫.||⃗݌ݏ‬ǁ^
‫ݓ‬ǁ cos ߜ;
⇒ (‫ݔ−ݔ‬‫ݏ‬) cosߠ + (‫ݕ‬ − ‫ݕ‬‫ݏ‬) sin ߠ ≥ √(‫ݔ‬ − ‫ݔ‬‫ݏ‬)2
+ (‫ݕ‬ − ‫ݕ‬‫ݏ‬)2
cos (ߙ/2) ; (2)
So far we have discussed the voronoi diagram and the sensing model for directional sensors. Due
to the limited sensing range of the directional sensors and random deployment, the target sensing
field is not fully covered and it leaves coverage holes in the field as shown in fig 12. Now we will
discuss the hole healing techniques to improve the coverage ratio for directional sensors using
voronoi diagram.
Figure 12. Random deployment of sensor nodes with their voronoi cells.[1]
3.1.1. Direction Adjustment
This technique is used for direction rotatable sensors. This means the directional sensors can
rotate 360o
and their working direction θ can be changed. In [1], three algorithms are proposed to
adjust the working direction of the sensors such that the overall coverage ratio of the network is
improved. Initially the sensor nodes are deployed randomly as shown in fig 12, then each node
starts constructing its voronoi cell with the information of its neighbor nodes. After the
construction of voronoi cell the three step algorithm works as follows:
• The sensor nodes calculate the area covered by them within their voronoi cell, when they
are allowed to face each vertex of the voronoi cell as shown in fig 13. The vertex with maximum
coverage area is selected and the working direction of the sensor is rotated towards that vertex.
Figure 13. Result of different vertex selection.[1]
During the calculation of the covered area, cases shown in fig 14 can arise. In fig 14a the covered
area is equal to the field of view of the sensor and can be calculated as:
As = (α/2)r2
; where As is called Intra-Cell Coverage Area.

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Now the intra-cell coverage area for other cases where field of view of the sensor extends through
the cell edges of the voronoi cell as shown in fig 14b,14c,14d, is calculated by dividing this area
into several triangles. The area of these triangles is summed up to get the final result.
Figure 14. Different cases of Intra-Cell Coverage Area.[1]
To calculate the area of different triangles, first the vertices of triangles are determined. The
vertices of triangles include those vertices of voronoi cell which comes inside the range or field of
view of the sensor node i.e. those voronoi cell vertices which satisfies eq1 and eq2. Also it
includes those points where voronoi cell edges intersect with the sector sideline or sector arc of
the field of view of sensor. The equation for the 2 sector sidelines is given as[1]:
(x-xs) cos θ + (y-ys) sin θ = √(x-xs)2
+ (y-ys)2
cos (α/2) ;
where √(x-xs)2
+ (y-ys)2
≤ r ;
The equation for the sector arc is given as[1]:
√(x-xs)2
+ (y-ys)2
= r ;
where x∈ [r cos (θ + α/2) + xs , r cos (θ – α/2) + xs] and y∈ [r cos (θ – α/2) + ys , r cos (θ + α/2) +
ys] ;
The equation for the voronoi cell edge is given as[1]:
x(ya - yb) = y(xa - xb);
√(x - xa)2
+ (y - ya)2
+ √(x - xb)2
+ (y - yb)2
= √(xa - xb)2
+ (ya - yb)2
;
where (xa,ya) and (xb,yb) are two vertices of the voronoi cell edge.
From these equations the intersecting points are obtained. After getting the vertices for triangles,
length of the three sides of each triangle is obtained and area of each triangle is calculated as[1]:
d=(e1 + e2 + e3)/2 ;
Area of triangle = √d(d-e1) (d-e2) (d-e3) ; where e1,e2,e3 are the three sides of the triangle. Now
this area for each triangle is summed up to get the intra-cell coverage area when a given voronoi
cell vertex is selected. The vertex with maximum value of intra-cell coverage area is selected as
the working direction of the sensor. This can be written mathematically as[1]:
Here ev
ij represents the jth
side of the ith
triangle when vertex v of the voronoi cell is selected, kv is
the total number of triangles for the vertex v, Vs is the set of vertices of the given voronoi cell and
vD is the vertex with maximum intra-cell coverage area. The working direction θ is calculated
as[1]:

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• The next step is to avoid coverage overlap, which can happen if multiple neighboring
sensor nodes selects the same common vertex as their working direction as shown in fig 15. Here,
sensor node with smaller intra cell coverage area can change its working direction. The condition
for this is given as[1]:
Here, Ns is the set of neighboring nodes who are adjacent to the voronoi cell of node s, vs
D is the
vertex selected as working direction for s, RvD
s is the coverage area or field of view of s when
vertex v is selected and AvD
s is the intra-cell coverage area of s when vertex v is selected. Now a
new set Us of vertices is defined as[1]:
Us = Vs – {vs
D} ; and to avoid overlap the new vertex selected as working direction for s is given
as[1]:
v’
D = argmaxvϵUs Av
s ;
Figure 15. Change in working direction to avoid common vertex and coverage overlap.[1]
In fig 15, we can see that sensor sj changes its working direction from v1 to v2 but still there is
some overlap. To avoid this a new set of vertices U`
s is defined as[1]:
This set of vertices includes those vertices which have smaller overlap than vD. Here, SvD is the
set of those sensor nodes except s whose working direction is vD and UsiϵSvD RvD
si is the union of
their coverage area or field of view. Now from set U`
s overlapped region is subtracted from intra-
cell coverage area of each vertex and the vertex with maximum value is selected for working
direction as[1]:
Here, Cv
s is the intra cell coverage region. As shown in fig 15 working direction is again turned to
vertex v6 to avoid the coverage overlap. If every vertex of the voronoi cell is selected by different
sensors as working direction, then the vertex with maximum coverage and minimum overlap is
selected as[1]:
Here sv is the other node which has selected vertex v as working direction.
• The third and last step is to avoid nodes from sensing outside the boundary of the field.
Nodes close to the boundary of the field may face towards the boundary which should be avoided.

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If the distance between the boundary of the field and the sensor τ is less than ωr where ω is the
coefficient between 0 to 1 then the working direction of the sensor is controlled between the two
limits θ1 and θ2 as shown in fig 16.
i.e. if τ < ωr; then 0≤θ≤θ1 and θ2≤θ≤2π ;
where θ1 and θ2 is calculated as[1]:
θ1 = [(π-α)/2] + sin-1
(τ/r);
θ2 = [(3π+α)/2] - sin-1
(τ/r);
Hence in fig 16 the choice for the working direction will be vertex vb and vc.
Figure 16. Avoiding coverage outside the boundary.[1]
3.1.2. Sensor Movement with Direction Adjustment
As the name suggest this technique is meant for the directional sensor nodes which have been
provided mobility. The sensor nodes can change their position and choose an optimal location,
from where coverage can be maximized. After getting the right location for movement, the
direction of the sensor can be adjusted. Initially sensor nodes are deployed randomly and they
start constructing their voronoi cell. Then the sensor node selects one of the voronoi cell vertex as
its new location as shown in fig 17.
Figure 17. Result of choosing different vertex as location.[2]
The vertex whose angle is greater than angle of view of the sensor and whose edges are greater
than sensing radius of the sensor is selected as new location for sensor movement. The angle β of
the vertex v is calculated by using the information about its left adjacent vertex vL and right
adjacent vertex vR as shown in fig 18. The coordinates of these adjacent vertices are (xL,yL) and
(xR,xR) respectively and angle β is calculated as[2]:

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Figure 18. Calculation of the angle β.[2]
Now a set of vertices T, which contains all those vertices of the cell whose angle β is greater than
or equals to angle of view α and whose edge length is also greater than or equals to sensing radius
r, is defined as[2]:
From this set T, a target vertex t is selected with maximum value for β as[2]:
If the set T is empty, then the target vertex is selected among all those vertices having β greater
than or equals to α and only one edge length greater than or equals to r. If we cannot find any
vertex satisfying these conditions then the vertex with largest value for β is selected.
Once the sensor is moved to the selected vertex, the working direction θ of the sensor is adjusted
within the limits θ1 and θ2 as shown in fig 19.
Figure 19. Calculation of the limits θ1 and θ2.[2]
To decide these limits θL and θR [2] are calculated which are defined as the angle of the vector
vvL
->
and vvR
->
with the positive x-axis respectively. θ1, θ2, θL, θR, [2] all lies between 0 and +-π.

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If the sensor is rotated towards the right side edge eR of the vertex v then θ1 will be the working
direction of the sensor and if sensor is rotated towards left side edge eL of the vertex v then θ2 will
be the working direction.
To improve the coverage ratio, sensor will be rotated towards the longest edge as shown in fig 20.
Figure 20. Cases of rotation of sensor.[2]
Let θ0 is the initial working direction of the sensor when it is moved to the vertex v, then the
extent or range φ to which θ0 should be rotated in either clockwise or anticlockwise direction
within the limits θ1 and θ2 is given as[2]:
3.2. Triangular Diagram Based Approach
In this technique every hole is healed by a single sensor node. A new node is deployed in the
region where hole is detected. In this process first the hole is detected then area of that hole is
calculated and thereafter the healing process starts. To heal a hole the area of the hole is required.
Area of the hole is calculated with the help of triangular diagram. This diagram is obtained by
joining the center points of every adjacent sensor node which as a result forms a triangle for every
three adjacent nodes in the network, see fig 21.
Figure 21. Triangular structure.[3]
Depending on the location of adjacent sensor nodes and distance between them several cases may
arise as shown in fig 22. Here, we can see the location of hole and intersection between adjacent
sensor nodes. s1,s2 and s3 is the area of intersection between the sensor’s sensing region and the
triangle.

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Figure 22. All cases for three adjacent sensors.[3]
In order to calculate the area of the hole, we have to do some calculations first. Let a,b,c be the
three sides of the triangles shown in different cases in fig 22. Then the area of these triangles
represented by s∆ is calculated as[3]:
s∆ = (1/4) √(a+b+c)(a-b+c)(b-a+c)(c-a+b) ;
and the relationship between region s1, s2 and s3 is given as[3]:
s1+ s2+ s3= (1/2)πR2
; where R is the sensing radius.
Now the area of the intersection of two circles or nodes represented by sintersect is calculated as
shown in fig 23. Here, two circles with different radius R, r and location (0,0), (d,0) respectively
are considered.
Figure 23. Calculation for the area of intersection of two circles.[3]
From fig 23, area of the intersection represented by A is given as[3]:
where A(r,d2) is the area of left portion of the intersection divided by line segment ‘a’ and A(R,
d1) is for the right portion. d1 and d2 is given as[3]:
Now in fig 22 sensor nodes are homogeneous, therefore here r=R and area of hole sh for all these
cases is thus calculated as[3]:
• For fig 22a,22b,22c,22h area is given by[3]:
sh = s∆ – (s1 + s2 + s3) ;

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• For fig 22d,22g area is given by[3]:
sh = s∆ – (s1 + s2 + s3) + (1/2)sintersect; and
• For fig 22e area is given by[3]:
• In fig 22f , hole doesn’t exist.
• For fig 22i area is given by[3]:
After calculating area of the hole, healing process starts. Each hole is healed by a single sensor
node. New sensor nodes are deployed in uncovered regions by following two methods:
• If the sensing area of the sensor is greater than area of the hole than circumcircle methods
is used as shown in fig 24. The circumcircle is obtained by the perpendicular bisectors of the
three sides of the triangle. The point where these perpendicular bisectors intersect is called the
circumcircle center of the triangle and this is the point where new nodes is deployed.
Figure 24. Calculation for circumcircle center of the triangle.[3]
• If the sensing area of the sensor is less than the area of the hole than incircle method is
used as shown in fig 25.The incircle is obtained by the angle bisectors of the three angles of
triangle. The point where these three angle bisectors intersect is called incircle center of the
triangle and this is the point where new node is deployed. The incircle is inscribed inside the
triangle and it is tangent to each side of the triangle.

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Figure 25. Calculation for incircle center of the triangle.[3]
3.3. Delaunay’s Triangulation
Delaunay’s Triangulation[8][18][19] is a geometrical structure which is formed by a given set of
points. It is a triangulation method in which triangles are formed in such a way that circumcircle
of each triangle will not contain any other point of the given set. This means the vertices of the
triangle will lie on the circumference of the circle and the circle will be empty inside. In fig 26(a),
the triangulation formed is Delaunay’s triangulation because each circumcicle is empty and 26(b)
is not Delaunay’s triangulation because each cicumcircle encloses a point inside it. Also the
minimum angle of a triangle formed by Delaunay’s Triangulation is maximum for other
triangulations for the same set of points.
Figure 26. Triangulation for a given set of four points. The minimum angle α shown in (a) is greater than
the minimum angle shown in (b).[8]
In[4], an algorithm is proposed to heal coverage holes using Delaunay’s triangulation as shown in
fig 27. Holes with irregular shapes and boundaries are analyzed and the point where the irregular
curve turns is considered as a vertex. All these vertices together form a closed polygon and then
the Delaunay’s triangulation is performed over the polygon vertices. The radius for the
circumcircle of the triangles formed is calculated and new node is deployed at the center of the
circumcircle whose radius is maximum.
Figure 27. Delaunay Triangulation of holes.[4]
2.4. Equally Divided Path Selection Method
This method says that new nodes should be patched along the angle bisector of the hole angle
discussed in section 2.5 for healing the hole. This path is the shortest path for data to travel to the
sink. To prove this, a hole Hi is considered inside a parallelogram TUVW as shown in fig 28. A
and B are two nodes equidistant and symmetrical from the sink. Let q is a point on AB and p is a
point on TU such that Aq=x, Bq=y, Ap=a, Bp=b and the distance between line AB and p i.e.
qp=h. Now using the property of a right angled triangle[6]:
a2
= h2
+ x2
;
b2
= h2
+ y2
;

17
Let a function f(x) = a+b; and AB=x+y=L;
=> f(x) = √ h2
+ x2
+ √ h2
+ (L-x)2
;
First and Second order derivative of f(x) is given as[6]:
Now by using maximum value theorem, the minimum value of x for the function f(x) comes out
to be L/2. This means minimum value for a+b will be obtained when x and y are equal i.e. q lies
in the center and passes through the angle bisector. Hence, the shortest path to reach sink through
the hole will be along the angle bisector. New nodes will be patched along this path.
Figure 28. Calculation for shortest path along the angle bisector.[6]
3.5. Comparative Study
The experimental results for direction adjustment and sensor movement with direction adjustment
is given in fig 29 and fig 30. The results shows that out of these two voronoi diagram based
healing techniques, sensor movement with direction adjustment is better. The results are obtained
for sensor nodes with angle of view α=120o
and sensing radius=50metres and field
size=500m*500m. This shows that providing sensor nodes with moving capabilities helps in
improving overall coverage of the network.
Figure 29. IDA represents Direction Adjustment.[1]

18
Figure 30. DVSA represents Sensor Movement with Direction Adjustment.[2]
The graph for Delaunay’s triangulation and equally divided path selection method is discussed
earlier in section 2.6. with fig 9 and fig 8, where they are implemented along with travelling
salesman method and weighted method. The equally divided path selection method is evaluated
in terms of average delivery hops whereas other methods are evaluated based on coverage ratio.
This is because equally divided path selection method focus on improving connectivity by
providing shorter routes to the active nodes in the network. A comparative study of these methods
is given in table 2.
Table 2. Comparative study for healing process methods.
Healing Process Method Mechanism Utility Type of Sensor
Network
Voronoi
Diagram
Based
Approach
Direction
Adjustment
Voronoi cell vertex is selected
as working direction of the
sensor.
Can be used
for both hole
detection and
Healing
Directional
Sensor Network
Sensor
Movement with
Direction
Adjustment
Voronoi cell vertex is selected
as the new location for the
sensor.
Triangular Diagram Based
Approach
New node is deployed either on
circumcircle center or incircle
center of the triangle, based on
the size of the hole.
Hole
Detection and
Healing
Omni-
Directional
Delaunay’s Triangulation
Method
Hole is divided into triangles
and new node is deployed on
circumcircle center of the
largest triangle.
Hole Healing Omni-
Directional
Equally divided path selection
Method
New nodes are deployed along
the angle bisector of the hole
angle.
Hole Healing Omni-
Directional
4. CONCLUSION
In this study, we discussed about various coverage problems and hole healing strategies in WSN.
It can be noticed that with the heterogeneity in sensor nodes we get different type of coverage
problems and hence will need different strategies to overcome these problems e.g. in mobile
sensor networks, coverage is improved by moving the sensors to appropriate locations, in
directional sensor networks, coverage is improved by adjusting the sensing directions of these
sensors, and in static sensor networks, we can patch failed nodes or can use redeployment
methods. The coverage holes can be healed in a random order or a proper sequence can be
followed. This sequence can be obtained by converting the problem into travelling salesman
problem, covering each hole once and returning back to the initial hole[4]. Priority healing is
another option where holes can be assigned a priority value based on some properties of the
hole[6]. All these techniques have their own advantages and disadvantages. Some algorithms are
centralized while others are distributed. The centralized algorithms results in optimal routes while
poses communication overhead. The distributed algorithms may not result in optimal routes but

19
they are energy efficient and can be used for scalable networks. Random healing result in
increasing the coverage ratio only while priority healing not only increases coverage but it can
also reduce energy consumption of the network during the healing process. Keeping in mind all
these factors we can choose an appropriate healing method suitable for our application.
REFERENCES
[1] T.-W. Sung and C.-S. Yang, (2013) “Voronoi-based coverage improvement approach for wireless
directional sensor networks”, Journal of Network and Computer Applications.
[2] T.-W. Sung and C.-S. Yang, (2013) “Distributed voronoi-based self-redeployment for coverage
enhancement in a mobile directional sensor network,” International Journal of Distributed Sensor
Networks, Article ID 165498, 15 pages.
[3] S. Babaie and S. S. Pirahesh, (2012) “Hole detection for increasing coverage in wireless sensor
network using triangular structure,” IJCSI International Journal of Computer Science Issues, vol. 9,
no.1, article 2.
[4] P. Si, C. Wu, Y. Zhang, Z. Xia, and L. Cheng, (2011) “A hole detection and redeployment strategy in
wireless sensor network,” Journal of Information and Computational Science, vol. 8, no. 13, pp.2577–
2585.
[5] C. Zhang, Y. Zhang, and Y. Fang, (2010) “A coverage inference protocol for wireless sensor
networks,” IEEE Transactions on Mobile Computing, vol. 9, no. 6, pp. 850–864.
[6] Fu-Tian Lin, Tien-Wen Sung, and Chu-Sing Yang, (2013) “A Coverage Hole Healing Strategy with
Awareness of Data Delivery Time in Wireless Sensor Networks,” International Journal of Distributed
Sensor Networks, Volume 2013, Article ID 790794, 11 pages.
[7] Waltenegus Dargie and Christian Poellabauer (2010) Fundamentals of Wireless Sensor Networks,
Theory and Practice; A John Wiley and Sons, Ltd., Publication.
[8] F. Aurenhammer, (1991) “Voronoi diagrams—a survey of a fundamental geometric data structure,”
ACM Computing Surveys, vol. 23, no. 3, pp. 345–405.
[9] Junbin LIANG, Ming LIU and Xiaoyan KUI, (2014) “A Survey of Coverage Problems in Wireless
Sensor Networks,” Sensors & Transducers, Vol. 163 , Issue 1, pp. 240-246.
[10] J. Yick, B. Mukherjee and D.Ghosal, (2008) “Wireless sensor network survey,” Computer Networks,
vol. 52, no. 12, pp. 2292–2330.
[11] F. Ye, G. Zhong, S. Lu and L. Zhang, (2002) “PEAS, a robust energy conserving protocol for long
lived sensor networks,” in Proceedings of 10th IEEE International Conference on Network Protocols
(ICNP’02), Paris, France, pp. 200-201.
[12] D. Tian and N. D. Georganas, (2003) “A node scheduling scheme for energy conservation in large
wireless sensor networks,” Wireless Communications and Mobile Computing, Vol. 3, Issue 2, pp.
271-290.
[13] J. Wu and S. Yang, (2004) “Coverage issue in sensor networks with adjustable ranges,” in
Proceedings of International Workshop on Mobile and Wireless Networking (MWN’04) in
conjunction with International Conference on Parallel Processing Workshops (ICPPW'04), Montreal,
Quebec, Canada, pp. 61-68.
[14] M. Cardei, M. Thai, Y. Li, and W. Wu, (2005) “Energy efficient target coverage in wireless sensor
networks,” in Proceedings of the 24th Conference of the IEEE Communications Society
(INFOCOM’05), pp. 1976-1984.

20
[15] Hang Ding Xing, Zhang Bo Yun and Tang Wen Shen, (2009) “Distributed connected algorithm for
wireless sensor networks,” Computer Engineering and Application, Vol. 45, Issue 7, pp. 17-19.
[16] I. Vasilescu, K. Kotay, D. Rus, M. Dunbabin and P. Corke, (2005) “Data collection, storage, retrieval
with an underwater sensor network,” in: Proceedings of the Third International Conference on
Embedded Networked Sensor Systems (Sensys), SanDiego, CA.
[17] Smita Karmakar and Alak Roy, (2014) “Holes Detection in Wireless Sensor Networks: A Survey,”
I.J. Modern Education and Computer Science, 4, 24-30
[18] D. Du, F. Hwang, S. Fortune, (1992) “Voronoi diagrams and Delaunay triangulations,” Euclidean
Geometry and Computers.
[19] ChunHsien Wu, KuoChuan Lee, YehChing Chung, (2006) “A Delaunay Triangulation Based Method
for Wireless Sensor Network Depoyment,” In Proceedings of the 12th International Conference on
Parallel and Distributed Systems, pp. 1521-1530
[20] A. Okabe, B. Boots, and K. Sugihara, (2000) Spatial Tessellations, Concepts and Applications of
Voronoi Diagrams, John Wiley & Sons, 2nd edition.
AUTHORS
Latesh Mehta is pursuing his Master degree in Computer Science Engineering from
Chitkara University, Himachal Pradesh, India. He is enrolled in Integrated Bachelor +
Master Degree course in Computer Science Engineering from Chitkara University,
Himachal Pradesh, India. His main research area includes, Wireless Sensor Network.
Manik Gupta is Assistant Professor in the Department of Computer Science at Chitkara
University, Himachal Pradesh, India. He has a good number of publications in the field of
wireless sensor networks in various international conferences and journals of good repute.
He had been awarded for Best Research Paper, in December, 2010. He also worked as
Software Developer for one year after completing his Bachelors in Engineering and as
Consultant in LSI, Research and Development. He also remained a regular columnist of
column “Manik’s Tech Tonics” in the newspaper- “Student Age”. His research area is Security, Energy
Efficiency, Fault Tolerance, Fault Revoking, Coverage, Connectivity and Mobility in Wireless Sensor
Networks and Body Area Sensor Networks.

REVIEW OVER HOLE HEALING TECHNIQUES IN WIRELESS SENSOR NETWORKS

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