Connected Point Coverage in Wireless Sensor
Networks using Robust Spanning Trees
Pouya Ostovari
Department of Computer
and Information Siences
Temple University
Philadelphia, Pennsylvania, USA
Email: ostovari@temple.edu
Mehdi Dehghan
Department of Computer Engineering
and Information Technology
Amirkabir University of Technology
Tehran, Iran
Email: dehghan@aut.ac.ir
Jie Wu
Department of Computer
and Information Siences
Temple University
Philadelphia, Pennsylvania, USA
Email: jiewu@temple.edu
Abstract—Energy limitation is one of the most critical chal-
lenges in the area of sensor networks. Sleep scheduling mecha-
nisms can reduce the energy consumption. Coverage mechanisms
attempt to cover the area with the minimum possible number of
sensors. There are many area coverage approaches which also
consider the connectivity problem. However, in the area of point
coverage, there are limited mechanisms that maintain connectiv-
ity. In this paper, we propose a point coverage mechanism and
two connectivity mechanisms. We compare these mechanisms
to one of the best methods that consider both point coverage
and connectivity. In the point coverage mechanism, we present
a method for computing the waiting time, which reduces the
number of the required sensors. For preserving the connectivity,
virtual robust spanning tree (VRST) and modified virtual robust
spanning tree (MVRST) are proposed. These mechanisms are
based on making a virtual spanning tree and converting this tree
to a physical tree. In order to spread out sensed data to the sink
from different paths and decrease the loss probability, instead
of using a minimum spanning tree (MST) to connect nodes to
the sink, we use a combination of distance of nodes and number
of hops to select edges and construct the tree. The simulation
results show that the proposed coverage method reduces energy
consumption by up to 7% compared to the Cardei method. The
VRST and MVRST use more energy than the Cardei method,
but the average data loss decreases by up to 40%. Moreover,
VRST and MVRST have less depth and data latency.
Index Terms—connectivity, energy efficiency, point coverage,
sensor network, sleep scheduling, virtual tree.
I. INTRODUCTION
Coverage is one of the most important challenges in the area
of sensor networks. Since the energy of sensors are limited,
it is vital to cover the area with fewer sensors. Generally,
coverage in sensor networks is divided into area coverage,
point coverage, and boundary coverage subareas. Coverage
does not ensure connectivity of nodes. However, many ap-
proaches have addressed both area coverage and connectivity,
but limited number of approaches have covered both.
Cardei proposed one of the best approaches in the field of
connected point coverage [1]. It contains two steps. Using the
first step, the sensing nodes are selected. In the second step,
some relay nodes are selected to make a MST between sensing
nodes and the sink, based on Prim’s algorithm, to ensure sink-
connectivity. However, MST has a problem. Usually, MST
is relatively deep. In addition, the sink does not have many
branches. Therefore, in the case of failure, we lose a significant
amount of data.
In this paper, we modify MST and we introduce a balanced
tree, which solves the problem of using MST to ensure
connectivity. In Prim’s algorithm, the cost of edges is the
distance of nodes. In contrast, our proposed method uses a
combination of distance and hop count as the cost of edges.
In the first step, we use a distributed algorithm to compute
the priority of nodes. This priority is computed based on
the residual energy of nodes and the number of targets in
their sensing area. Nodes with more residual energy and more
targets in their sensing area have more priority than other
nodes. In the second phase, we use another algorithm to select
some relay nodes to construct a balanced tree between sensing
nodes and the sink. To construct the tree, we first construct
a virtual tree with targets and the sink, which is used as a
skeleton to built an actual tree. After making a virtual tree, we
convert it to a physical tree between nodes that are selected
in the covering phase as a sensing node and the sink.
In comparison to the Cardei method, our proposed method
uses less sensors to cover all targets. In addition, our proposed
method is more balanced than the Cardei method; therefore, in
the case of node failure, we will lose less data, as all branches
are more balanced. However, our proposed trees uses more
relay nodes to deliver sensed data to the sink, so the probability
of a node failure in our tree is more of that the Cardei method.
The contributions of this paper are the following:
• We change one of the existing point coverage methods
to reduce energy consumption of sensor nodes.
• To maintain connectivity, we propose a method to con-
struct a balanced tree which is more robust against failure.
• We consider and avoid cycle formation which might
happen during converting virtual trees to physical trees.
The remainder of the paper is organized as follows: Section
2 presents related works on connectivity and coverage. In
Section 3, we present our proposed methods. Simulation
results are shown in Section 4.
II. RELATED WORKS
A survey on coverage problems in wireless sensor networks
is presented in [2]. The coverage problem is divided into three
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DOI 10.1109/ICDCSW.2011.47
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DOI 10.1109/ICDCSW.2011.47
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subcategories: area coverage, point coverage and boundary
coverage.
Most of the research in the field of sensor networks consists
of area coverage. The goal of area coverage is to cover as much
area as possible with the minimum number of sensors. Most
of these researches use probabilistic or geometric approaches.
It is shown in [3] that the problem of selecting a subset
of sensors that cover the whole area is NP-Complete, and
the authors proposed an efficient approximation algorithm to
address area coverage. [4] proves that if the radio range is
at least twice the sensing range, complete coverage of a area
implies connectivity among the working set of nodes. In ACOS
[5], each node computes the area which can be only covered
by it. If this area is smaller than a threshold, then this node
goes to active mode.
The goal of point coverage is to cover some specific points
of the network. [6] proposes an efficient method to extend
the sensor network lifetime by organizing the sensors into a
maximal number of disjoint sets that are activated successively.
It is shown in [7] that selecting disjoint sets do not necessarily
result in a larger lifetime of the network than non-disjoint
sets. In this approach, the nodes are organized into maximal
numbers of set covers instead of disjoint-sets. [8] addresses
the target coverage issue in wireless sensor networks that
have sensors with adjustable sensing range. To solve this
issue, linear programming, a localized greedy algorithm, and
a distributed greedy algorithm, are proposed.
In the boundary coverage problem, the goal is to cover the
network so as to minimize the probability that a mobile object
which cross the barrier of network remains undetected. It is
illustrated in [10] that the best path for an intruder from a
source to a destination is in the Voronoi diagram. [11] supposes
that the view field of sensor nodes is limited and sensors a have
a directional camera. An optimal polynomial time algorithm
was presented for computing the worst-case breach coverage.
Breach is the maximal distance that any hostile target cannot
be detected by the sensors while traveling through a region.
[12] studies the trade-off between the number of sensors and
the breach detection probability.
The studies that are more relevant to our approach are [1]
and [9]. [9] presented a distributed approach for the con-
nected point coverage problem of wireless sensor networks.
This approach selects a dominate set of sensors to serve
as a backbone to ensure connectivity. In addition, it uses a
distributed algorithm similar to [8] to cover all targets. [1]
uses a distributed algorithm to select sensing nodes. During
the second phase, it selects relay nodes. For this purpose, it
makes a virtual tree between targets and the sink and then
converts it to a physical tree of sensing nodes and the sink.
Our work is an improvement of [1]. We changed the
coverage method to reduce the number of active sensors that
are needed to cover all of the targets. Instead of using MST to
maintain sink-connectivity, we use a balanced tree to decrease
the amount of data loss in sensor networks.
III. OUR APPROACH
In this section we propose our distributed method for
connected point coverage, which is based on the Cardei
method. We want to cover some targets in a homogeneous
sensor network, using an efficient number of sensors while still
preserving sink-connectivity. Nodes and targets are stationary
and we suppose that each node knows the location of all targets
and the sink.
The algorithm runs in rounds. Each round begins with an
initialization phase in which every sensor decides whether to
be active or inactive for the rest of the round. This phase
is divided into two steps: In the first step, sensing nodes
selection, the sensor nodes are selected such that the union
of them covers all the targets. In the second step, relay nodes
selection, additional relay nodes are chosen so as to guarantee
sink-connectivity. These steps are explained in the following
sections.
A. Sensing Nodes Selection
In this phase a set of efficient sensing nodes is selected to
cover all the targets in the field. Since this problem is NP-
complete [1] we use a distributed greedy heuristic to address
it. We start from selecting sensors with more targets in their
sensing area and more residual energy as sensing nodes and
we keep doing it until covering all the targets. To make this
heuristic distributed, each sensor node computes a waiting time
based on its residual energy and the number of uncovered
targets it can cover. We use these waiting times to select
sensing nodes in increasing order of their priority. The sensor
that covers more uncovered targets and has more residual
energy will get less waiting time, and thus more priority than
other sensors. The waiting time of a sensor s
u
is computed
by the equation (1):
T
u
= (1 − α ∗
E
′
u
E
− β ∗
|T argetS
u
|
M
) ∗ W
1
− T
′
u
(1)
where:
• E
′
u
: the residual energy of sensor s
u
• E: the initial energy of sensors
• M : the number of targets in the network
• W
1
: the maximum waiting time
• α,β: weights which are assigned to the residual energy
and the number of uncovered targets
• T argetS
u
: Targets which are in sensing range of node
s
u
and have not been covered by any sensor node yet
• T
′
u
: the waiting time which sensor s
u
has passed
When the waiting time of a sensor s
u
is finished, it is
selected as a sensing node and it acts as the supervisor of
all the targets in the set T argetS
u
. The supervisor of a target
is the first sensor that passed its waiting time and covers it.
Next, this sensor broadcasts a notification message to inform
its neighbors about the targets covered by it.
When a sensor passing its waiting time receives a notifica-
tion message from its neighbors, it updates its waiting time
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and the set T argetS
u
if it has at least one target within its
sensing range in common with the targets mentioned in the
message. Assuming that R
S
is the sensors’ sensing range
and R
c
is the sensors’ communication range, the maximum
distance between two sensors with a common target in their
sensing range is 2R
S
, if R
S
< 2R
C
. Therefore, it is adequate
to broadcast the notification message in two hops.
The basic difference between our proposed method for
sensing nodes selection and the Cardei method is that in the
former the elapsed waiting time of a sensor is not considered
in re-computation of the waiting time when it receives a
notification message. As a result, sensors with a high number
of targets in common with other sensors must update their
waiting time many times, so their priority decreases and their
waiting time increases each time, regardless of the time that
passed up until now.
B. Relay Nodes Selection
After selecting sensing nodes and covering all the targets,
relay nodes must be selected to provide sink-connectivity. We
suppose here that each sensor knows the location of the sink
and all the targets.
Achieving sink-connectivity, each selected sensing node s
u
makes a virtual tree based on the set of targets and the sink.
Unlike the Cardei method, which uses Prim’s algorithm to
construct a virtual minimum spanning tree, we use a modified
version of robust spanning tree [13] in order to make our
approach robust against failure of nodes. In this spanning tree,
which we call a virtual robust spanning tree (VRST), the root
is the sink and other vertices are targets. This tree serves as a
virtual skeleton for the considered network. In order to convert
this virtual tree to a physical tree of sensors, each sensing node
broadcasts a message to find the supervisor of the target which
is the parent of its covered target.
The VRST algorithm is similar to Prim’s algorithm, but
rather than using the edge’s length (edge’s cost) for choosing
an edge, it uses a combination of the edge’s length and the
vertex’s depth (hop count). Here, we assume that the edge’s
length is Euclidean distance between connecting points. In this
algorithm, cost is computed as follows:
Cost = λ ∗ hop count + (1 − λ) ∗ (weight of path
i
), (2)
which λ is a function of the depth of a vertex:
λ
i
= 1 −
h
i
ǫ
1
(3)
weight of path
i
= weight of path
j
+ z
i,j
(4)
Descriptions of notations are as follows:
• hop count: number of hops to the sink
• weight of path
i
: sum of the edges’ cost which connect
vertex i to the sink
• ǫ
1
: depth of the MST (maximum hop count)
• h
i
: depth of vertex i
Sink
Target
Sensors
Virtual links
(a) (b)
Fig. 1. Examples of virtual trees in (a) MST and (b) VRST
• z
i,j
: length of edge (i, j)
In relay node selections, we first construct a MST based
on the set of targets and the sink, using the Prim’s algorithm,
and we set ǫ
1
to the depth of this tree. Subsequently, cost is
computed for each vertex and for the edges which connect it
to a vertex of the tree according to equation (2). The vertex
connected to the edge with the minimum cost is selected and
added along with this edge to the tree.
The closer a vertex is to the sink, the greater λ it will have.
Therefore, the edge’s length has a greater effect on computing
the edge’s cost. As a result, vertices nearer to the sink will
directly connect to it yielding a fat tree around the sink. On
the other hand, vertices farther from the sink will have more
choices to connect. As a result, the depth of the tree will
decreases. Farther vertices have smaller λ, so the path weight
has more of an effect on their edges’ cost. Thus, these vertices
will connect to the tree along edges which connect them to
the path with the minimum cost.
Figures 1(a) and 1(b) show a MST built with Prim’s
algorithm and a VRST, respectively. Obviously, the depth of
the VRST is far less than the MST.
As said before the supervisor of a target is the first sensor
that passed its waiting time and covers it. After constructing
the virtual tree, supervisors of targets must connect together
via physical paths. Therefore, we have to select some relay
nodes to connect the supervisors of targets. For each target t
i
,
the sensing node s
u
starts the selection of relay nodes along
the virtual link (t
i
, π(t
i
)), where π(t
i
) is the parent of target
t
i
in the virtual tree.
Every sensing node s
u
broadcasts a control message
RELAY
REQ for each target under its supervision. This
message contains the location of sensing node s
u
, destination
target π(t
i
), and the maximum distance from sensing node
s
u
to the supervisor of target π(t
i
). The maximum distance
of two supervisors can be calculated using equation (5). Each
sensor that receives this message computes its distance from
the source sensor. If this distance is less than the maximum
distance mentioned in the message RELAY
REQ, then it
forwards the message.
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Sink
Target
Sensors
Virtual links
Physical links
(a) (b)
Fig. 2. Examples of virtual and physical trees in (a) Cardei and (b) VRST.
Max distance = distance(t
i
, π(t
i
)) + 2R
s
(5)
When the supervisor of target π(t
i
) receives the message
RELAY
REQ, it will reply to this message. It will send
this reply message to the sensing node s
u
, through one of the
pathes in which it received the message RELAY
REQ. The
supervisor of target π(t
i
) can select one of the relay sensors
who delivered the message RELAY REQ, based on one of
the following criteria:
• Relay sensor closest to the node s
u
• The first relay node which delivered the message
• Relay node with the most residual energy
This procedure will continue until the reply message is
delivered to the source sensing node. Consequently, a physical
path is built between sensing nodes and the sink. All nodes
participating in delivering the reply message are chosen as
relay nodes.
In Figure 2, virtual trees made by the Cardei method, the
VRST method, and physical trees built based on them are
shown. It can be seen in this figure that the physical tree made
based on the VRST method, has less depth and more paths to
the sink compared to the physical tree made based on MST.
Therefore, in our proposed method, we will have less data loss
when a sensor node fails.
In equation (4), the cost of connecting vertex (target) i
to vertex j as a member of the tree is equal to the sum of
the length of edge (i, j) and the path’s wight from vertex j
to the sink. Hence, in addition to the direct effect of depth
on equation (2) as hop count, it indirectly affects the path
weight from vertex j to the sink; thus, it has a double effect
on this equation. In other words, not only is the vertex’s
depth important to vertices near the sink, but also important
to the vertices far from it. Its immediate result is that the
vertex’s depth has a more important role than the edge’s length
in selecting edges. For this reason, in the second proposed
method (MVRST), for relay nodes selection, we ignore the
weight of path from vertex j to the sink and we consider the
(a) (b)
Sink
Target
Sensors
Virtual links
Physical links
Fig. 3. Examples of virtual and physical trees in (a) MVRST and (b) VRST.
1 1
2
2
3 3
1
2
3
4
1
2
3
4
(a) (b)
Fig. 4. Forming cycles during converting virtual trees to physical trees.
weight of edge (i, j) as the weight of the path from vertex i
to the sink:
weight of path
i
= z
(i,j)
(6)
As shown in Figure 3, virtual and physical trees made by
the MVRST method have less depth than trees made by the
VRST method.
C. Avoiding Cycle Formation
Since some of the sensing nodes cover more than one target
and are supervisors of some or all of them, it is possible that
while we are converting a virtual tree to a physical tree, cycles
are formed. This happens when a sensing node is a supervisor
of more than one target and these targets have different parents.
These cycles could have a length greater than or equal to two.
In Figure 4(a), a cycle with a length of two is shown. Sensor
2 covers two targets whose parents are different. If this sensor
chooses sensor 3 as its parent during the conversion from
virtual to physical tree, a cycle will be formed between sensors
2 and 3.
In order to avoid cycles with length of two, when a sensing
node s
u
, which is supervisor of more than one target, wants
to select sensing node s
j
as its parent, it must check if it has
received any RELAY
REQ message from node s
j
that its
destination is node s
u
. Receiving this message means that it
is possible that sensing node s
j
selects sensing node s
u
as its
parent, and in this case, a cycle with a length of two will be
formed. For cases with a length more than two, we could use
two approaches:
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70 80 90 100 110 120
2800
3200
3600
4000
Energy Consumption (mw/h)
Sensing Range (m)
Cardei
MVRST
Fig. 5. Effect of sensing range on energy consumption: R
c
= 120m
• Using cycle detection algorithms: Sensors covering more
than one target run a cycle detection algorithm. If they
detect a cycle, they choose another sensor as their parent.
• Packet examination: Sensors send their packets in one
of the existing paths. A returned packet to its source
indicates that there is a cycle in the network, and this
sensor should change its parent.
/bf We used packet examination approach in our proposed
methods, since it is more efficient than cycle detection ap-
proach. The reason is that the computational cost of cycle
detection algorithms is high, which is O(n
3
), and the prob-
ability of formation of cycles with length more than two is
low (as observed in simulations, less than 5 cycles in 1000
run times).
IV. SIMULATION RESULTS
In this section we setup a set of simulation experiments
to compare the performance of our proposed methods with
that of the Cardei method. For this purpose, we implemented
a simulator in the environment of MATLAB. We considered
a stationary network in which sensor nodes and targets are
scattered randomly in a square field 500m × 500m. Other
simulation parameters are as follows:
• 500 sensors.
• 50 targets.
• Sensing energy consumption in a range of 50m is
20mW/s.
• Communication energy consumption in a range of 80m
is 60mW/s.
For sensing and communication ranges greater than the
specified ranges, we compute energy consumption as a square
power. All sensors are homogeneous, so they have equal
sensing and communication range. For each scenario, we
executed simulations 200 times and we showed the average
outputs in charts.
In the first experiment, we compared our proposed coverage
method with the Cardei coverage method. In both methods
we used the same relay nodes selection scheme, proposed by
70 80 90 100 110 120
3200
3600
4000
4400
Energy Consumption (mw/h)
Sensing Range (m)
Cardei
MVRST
VRST
Fig. 6. Effect of sensing range on energy consumption: R
c
= 120m
Cardei. Energy consumption of all the nodes, as shown in
Figure 5, is the sum of energy consumption of sensing nodes
and relay nodes. In this figure, the communication range is
120m. It can be seen that energy consumption of our proposed
coverage method is less than that of the Cardei coverage
method. The difference between these methods increases by
increasing the sensing range. The reason is that by increasing
the sensing range, the number of common targets covered by
distinct sensors increases.
In Figure 6, we compared the VRST and MVRST methods
against the Cardei method. In this figure we combined our pro-
posed coverage method with the VRST and MVRST methods.
Since the VRST method gives more priority to the depth of the
virtual tree and tries to decrease it, the number of relay nodes
and consequently energy consumption of this method is more
than that of others. The Cardei method has the least energy
consumption, since it uses a MST for relay nodes selection.
Finally, as the MVRST method gives more importance to
energy consumption during the construction of the virtual tree,
whereas the VRST method, its energy consumption is less.
Notice in Figure 6 that the energy consumptions of the VRST
and MVRST methods are decreased more than the Cardei
method by increasing the sensing range. As mentioned before,
the reason is that by increasing the sensing range, the effect
of our proposed coverage method increases.
In Figures 7 and 8, we compared the maximum and average
data loss of our proposed methods with that of the Cardei
method in a scenario of a single node failure. As expected,
the maximum and average amount of data loss in the Cardei
method is significantly more than the VRST and MVRST
methods, since the Cardei method does not consider the depth
of the tree and the number of transmission paths to the sink. It
can be observe in Figure 7 that there are some critical nodes
in the Cardei method, which their failure will result in a loss
of more than 95% of sensed data.
Figures 9 and 10 illustrate the effect of communication
range on the maximum and average data loss. In these figures
the slope of all charts is almost zero. This is because that
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