Sensor Scheduling for kCoverage in Wireless
Sensor Networks
Shan Gao,Chinh T.Vu,and Yingshu Li
Department of Computer Science
Georgia State University
Atlanta,GA 30303,USA
{sgao,chinhvtr,yli}@cs.gsu.edu
Abstract.Some sensor network applications require kcoverage to en
sure the quality of surveillance.Meanwhile,energy is another primary
concern for sensor networks.In this paper,we investigate the Sensor
Scheduling for kCoverage (SSC) problem which requires to eﬃciently
schedule the sensors,such that the monitored region can be kcovered
throughout the whole network lifetime with the purpose of maximiz
ing network lifetime.The SSC problem is NPhard and we propose a
heuristic algorithm for it.In addition,we develop a guideline for users to
better design a sensor deployment plan to save energy by employing den
sity control.Simulation results are presented to evaluate our proposed
algorithm.
1 Introduction
Sensor networks which usually consist of a large number of sensors are attract
ing people’s attentions.They can sense and collect information from all kinds
of objects in the monitored area.Furthermore,they can process the gathered
information and send it back to users.Therefore,they are being widely employed
for military ﬁelds,national security,environmental monitoring,traﬃc control,
health,industry,disaster prevention and recovery [1].However,current sensor
networks still have some limitations that prevent them from better serving the
people.The limitations are as following:limited power at each sensor,limited
communication ability,limited computation ability,limited wireless bandwidth,
large number of nodes in a network,huge deployment area and inﬁnite sensing
data streams.These limitations bring a lot of challenging problems.In this pa
per,we address the kcoverage problem which requires that every point of the
whole monitored area can be covered by at least k sensors at any time.
To deploy a sensor network,an aircraft may be used to spread the sensors
into an area when ground access is not possible.This causes the lack of accurate
placement of sensors,which will be compensated by deploying more redundant
sensors.Another reason for deploying redundant sensors is to provide fault
tolerance,since sensors are prone to failures [1].If any point in the monitored
area is monitored by at least k sensors,proper operation of the network can
still be ensured,even if some sensors fail.The required coverage level k may
J.Cao et al.(Eds.):MSN 2006,LNCS 4325,pp.268–280,2006.
c
SpringerVerlag Berlin Heidelberg 2006
Sensor Scheduling for kCoverage in Wireless Sensor Networks 269
be diﬀerent for diﬀerent applications.In friendly environment such as home
monitoring,k can be set to a small value,while in hostile environment such as
battle ﬁelds,k should be set to a large value.Even for a single sensor network,k
may be diﬀerent.For example,for forest ﬁre detection,k may be low in the rainy
season,but high in the dry season.One may say that since much redundant
sensors are deployed,the kcoverage problem can be easily solved.However,
considering the power limitation of sensor networks,to make all sensors remain
active greatly shortens the network lifetime.It is shown in [2] that each sensor
spends 0.34W to 0.7W power when it is in the transmit,receive and idle states,
however,only 0.03W in the sleep state.In addition,the lifetime of a battery
discharging in short bursts with signiﬁcant oﬀtime is approximately twice as
much as that in a continuous operation mode [3].These facts indicate that a good
active/sleep scheduling mechanism can dramatically extend network lifetime.
Therefore,while maintaining the coverage level k,only a subset of the sensors
is needed to be active at any time.
In this paper,our contributions are as following:i) we deﬁne the problem
of Sensor Scheduling for kCoverage (SSC) which is NPhard;ii) we design a
heuristic algorithm for the SSC problem which divides the sensors into subsets,
such that a schedule can be worked out by activate these subsets successively to
extend network lifetime;and iii) we propose a density control scheme for sensor
deployment to reduce the number of unallocated sensors such that the network
eﬃciency is improved.
2 Related Work
Recently,the coverage problem,a fundamental problemin sensor networks about
how well an area is monitored by sensors,has attracted people’s attentions.
Basically,there are three kinds of coverage problems [6] which are target coverage
problem,area coverage problem and breach coverage problem.The work in [7]
∼ [8] addressed the target coverage problem where the purpose is to cover all
the targets.The work in [4],[5],[9] ∼ [11] addressed the area coverage problem
where the purpose is to cover the whole monitored area.The breach coverage
problem is addressed in [12] where the purpose is to minimize the number of
uncovered targets.Some other work,[14] and [15],tried to ﬁnd a path which
is best or worst monitored by sensors and connects two given points inside or
outside the surveillance area and this path can indicate the sensing ability of the
sensor network in the best or the worst situation.
None of the above work considers the kcoverage requirement for the purpose
of quality of surveillance.To the best of our knowledge,not much work address
the kcoverage problem.Wang et al.[9] ﬁrst studies this problem.The coverage
levels of all the intersection points are determined through verifying the coverage
degrees of the area.They proposed a localized heuristic for constructing a cover
set (subset of sensors) that can provide kcoverage.However,the size of the
obtained subset cannot be guaranteed to be small.In [5],the authors designed
a greedy heuristic for the kcoverage problem and the size of their constructed
270 S.Gao,C.T.Vu,and Y.Li
cover set is within O(logn) factor of the optimal.The main idea is to select
a candidate path which has the maximum KBeneﬁt value.Both of these two
work only consider constructing one cover set instead of dividing sensors into
subsets such that each subset can provide kcoverage.In [13],the authors study
the sensor deployment problem so that kcoverage can be guaranteed.
In [4],the coverage problem is formulated as a decision problem,whose goal
is to determine whether each point in the monitored region is covered by at
least k sensors.The main idea is to check the perimeter coverage level of each
sensor.They prove that the whole monitored region is kcovered if and only if
each sensor in the monitored region is kperimetercovered.Based on this work,
we design in this paper a heuristic algorithm to divide the sensors into subsets
and each of the subset can provide kcoverage,such that the network lifetime
can be maximized.
The diﬀerences between these algorithms and ours are:1) our algorithms
provide solutions to kcover the monitored area;2) in our algorithms,kcoverage
is 100% guaranteed;3) there is no limitation on sensor’s sensing range which
could vary in a range instead of several ﬁxed values;4) our algorithms have no
limitation on the number of sensors and the sensor positions.
3 Sensor Scheduling for kCoverage
We consider a sensor network which monitors a two dimensional region and no
two sensors are located at the same location.Every point in the region needs to
be continuously monitored (covered) by at least k sensors.The network lifetime
is deﬁned as the total duration during which the whole region is kcovered.We
assume the number of the deployed sensors is more than the required number
of sensors that can provide kcoverage for the monitored region.To extend the
network lifetime,instead of making all the sensors to be active throughout the
whole network lifetime,a subset of the sensors can be turned on to provide k
coverage at any time,while the rest sensors are in sleep mode.We also assume
the transmission range of a sensor is at least twice the sensing range of a sensor
so that connectivity is also guaranteed within each subset [9].All the sensors
have uniform transmission range and sensing range.Then the problem of sensor
scheduling for kcoverage can be deﬁned as following.
Deﬁnition 1 Sensor Scheduling for kCoverage (SSC):Given a sensor
network with n sensors that can provide kcoverage for the monitored region,
schedule the activities of the sensors such that at any time,the whole region can
be kcovered and the network lifetime is maximized.
In [5],the authors consider the problem of constructing a single connected k
coverage set and this problem (CCP) is proved to be NPhard.Therefore,the
SSC problem is NPhard since CCP is a special case of the SSC problem when
the number of the constructed kcoverage sets is one.The scheduling decisions
can be made at the Base Station (BS).The BS broadcasts the schedule to all
the sensors so that each sensor can know when it should be active to monitor
Sensor Scheduling for kCoverage in Wireless Sensor Networks 271
the region.To solve the SSC problem,we can divide the sensors into disjoint
subsets.Each subset can kcover the whole region,where kcover indicates for
every point in the monitored region,at least k sensors can cover this point.These
subsets can be scheduled to be active successively.For each subset,its lifetime
is decided by the sensor which has the least power.Therefore,the lifetime of the
entire network highly depends on the number of subsets.
The following notations are used to formulate the SSCproblemand to describe
our algorithm.
– K:If all the sensors are active,any point in the monitored region can be
covered by at least K sensors.
– k:k (k ≤ K) is a userspeciﬁed parameter which speciﬁes the required
coverage level the sensor network must provide at any time.
– S:The set of all the sensors.
– m:All the sensors can be divided into at most m subsets and each subset
can kcover the monitored region.
– C
i
:The ith subset,1 ≤ i ≤ m.
– cov
i
:The coverage level of the C
i
,which means any point in the monitored
region is covered by at least cov
i
sensors which belong to C
i
.
Our goal is to construct as many subsets as possible such that i) each subset
can kcover the whole monitored region;ii) the network lifetime is maximized.
Then the SSC problem is formulated as
Objective:Max m
Subject to:
1≤i≤m
C
i
⊆ S
C
i
∩ C
j
= ∅,1 ≤ i,j ≤ m,i
= j
cov
i
≥ k,1 ≤ i ≤ m
4 Disjoint Cover Sets with Fixed Sensing Range
In this section,we present a greedy heuristic for the SSC problem.In [4],the
authors proved that the entire monitored region is kcovered if and only if each
sensor in the monitored region is kperimetercovered.kperimetercover requires
that any point on the perimeter of a sensor i be covered by at least k sensors other
than sensor i.Based on this fact,we propose a greedy algorithm,PCLGreedy
Selection (GS).We deﬁne the Perimeter Coverage Level (PCL) of a sensor a as
the number of the sensors in the same set that cover any point on a’s perimeter
of the sensing area.The lower the PCL is,the smaller the node density (the
number of nodes per unit area) is.
The main idea of GS is to iteratively construct subsets C
i
by choosing sensors
from the area with the lowest sensor density.When construct an individual C
i
,
the sensor with a smaller PCL value will be added to C
i
at each step.In this way,
we can include as less sensors as possible in C
i
and these sensors are distributed
in the area as widely as possible,such that more sensors can be left to join
272 S.Gao,C.T.Vu,and Y.Li
Algorithm 1.PCLGreedySelection(k,S)
1:Sort S in nondecreasing order based on their PCL values
2:while S is not empty do
3:cov
i
←getCoverageLevel(C
i
)
4:if cov
i
< k then
5:node ←the ﬁrst sensor in S
6:Add node to C
i
7:Remove node from S
8:else
9:PruneGreedySelection(k,S,C
i
)
10:Add C
i
to C
11:i ++
12:end if
13:end while
14:output C
other subsequent subsets and the overlapped sensing regions in each subset are
reduced as much as possible.This also indicates when construct a subset C
i
,the
area with smaller node density is taken care of with higher priority.
The GS is shown in Algorithm 1..The input includes k,a userspeciﬁed cov
erage level,and S,the set of all the sensors.The output is a collection of subsets
C,and each subset can kcover the whole monitored region.To justify if a subset
C
i
can kcover the entire monitored region,we can use the method proposed in
[4] and we call it getCoverageLevel(C
i
).Firstly,all the sensors in S are sorted
in nondecreasing order based on their PCL values.Then sensors are added to
a subset in a greedy manner.If at some iteration,the current subset C
i
can
provide kcoverage,a new subset C
i+1
will be constructed in the same manner.
GS stops when we can no longer construct a subset that can kcover the whole
monitored region.
Since each subset is constructed in a greedy manner,it is possible that there
exist some redundant sensors in a subset.Therefore,after constructing a subset,
we need to remove those redundant sensors and add them back to S so that they
are still available to be added to the subsequent subsets.The algorithm to con
duct this operation is PruneGreedySelection which is described in Algorithm
2..In this algorithm,given a subset C
i
,we check for each sensor in C
i
to see if
the removal of it will make cov
i
smaller than k.If a sensor is redundant (after
the removal of this sensor,cov
i
is still no less than k),it will be added back to S.
In [4],the authors have shown the fact that if no two sensors are located at the
same location,the whole monitored region is kcovered if and only if each sensor
is kperimetercovered.Based on this fact,the correctness of our algorithm is
guaranteed.
Theorem 1.The time complexity of GS is O(n
2
dlog(d)).Here,n is the number
of the sensors,and d = max(d
1
,...,d
i
,...,d
n
) where d
i
is the number of neighbors
of sensor
i
.
Sensor Scheduling for kCoverage in Wireless Sensor Networks 273
Algorithm 2.PruneGreedySelection(k,S,C
i
)
1:for j = 1 to C
i
 do
2:s
j
←the jth sensor in C
i
3:Remove s
j
from C
i
4:cov
i
←getCoverageLevel(C
i
)
5:if cov
i
≥ k then
6:Add s
j
to S
7:else
8:Add s
j
back to C
i
9:end if
10:end for
Proof.The time for sorting S is O(nlogn).There are n iterations in the while
loop.At each iteration,the main part that dominate the time complexity is
getAreaCoverageLevel or PruneGreedySelection.The function,
getAreaCoverageLevel,is proposed in [4].Its time complexity is O(C
i
dlog(d)),
where C
i
 is the size of a subset C
i
.The time complexity for
PruneGreedySelection is O(C
i

2
dlog(d)).Therefore,the time complexity of
GS is O(n
2
dlog(d)).
The number of the subsets constructed by GS decides the network lifetime.The
following theorem gives the bound of the number of the constructed subsets in
the ideal cases.
Theorem 2.Given some sensors Kcovering an area,if the sensors’ sensing
range is ﬁxed and the constructed subsets are disjoint,the maximum number of
subsets m is
K
k
,where K (K ≥ k) is the minimum coverage level that the
sensor network can provide if all the sensors are activate.
Proof.If the minimum coverage level provided by a sensor network is K,there
exists some point a in the monitored region such that there are K sensors that
can cover a.After the ﬁrst subset is constructed,there are K − k candidate
sensors that can cover a.By repeatedly constructing subsets,ideally at most
K
k
subsets can be constructed so that each of them can k cover a,that is,to
guarantee kcoverage for the whole monitored region.Thus,
K
k
is the upper
bound of m.The lower bound of m is
K
k
too.To prove this,without loss of
generality,we assume m=
K
k
−α.Then,after allocating sensors into
K
k
−α
subsets,the remaining sensors should be able to (K −
K
k
k + αk)cover the
monitored area in ideal cases.Because (K −
K
k
k) ≥ 0,the remaining sensors
could construct α more subset(s).This leads to a contradiction.Thus,the lower
bound of m is
K
k
too.Based on the upper bound and the lower bound of m,
we conclude that m=
K
k
.
5 Density Control of the Sensor Deployment
From Theorem 2,we can see there is a linear relationship between K and the
number of the constructed subsets.This is also validated through the simulation
274 S.Gao,C.T.Vu,and Y.Li
results in Section 6.As the network lifetime is decided by the number of the
constructed subsets,to have a longer network lifetime,K should be larger which
indicates the total number of the sensors should be larger.Another factor that
may aﬀect the network lifetime is the sensor density which is deﬁned as the
number of sensors in each unit area.Diﬀerent areas in a monitored region have
diﬀerent sensor densities.Fromthe simulation results,we found that there always
exist some sensors that were not allocated to any subset which is a waste of
resource.The waste is due to the diﬀerence between the sensor density of the
area near the border of the monitored region and the sensor density of the area
at the center of the monitored region.The unallocated sensors are usually the
ones at the center of the monitored region.The sensors near the borders have
smaller PCL values and the sensors at the center have larger PCL values.GS
adds sensors to a subset beginning from the sensors with smaller PCL values.
Thus,it is possible after all the sensors near the border have been added to some
subsets,there still exist some sensors at the center and no more subsets can be
constructed to provide kcoverage for the whole monitored region.Therefore,to
extend the network lifetime,the PCL values of the sensors need to be balanced,
so that the closer to the border the area is,the more sensors this area should
have.To guarantee balancing the PCL values,the number of the neighbors of
the sensors’ close to the borders should be equal to the number of the neighbors
of the sensors at the center.We derive a relationship between the sensor density
of the area near the border and the sensor density of the area at the center in
Theorem 3.We deﬁne a disk centered at c as D
c
.The sensor density of D
c
is
denoted as ρ
c
,and
ρ
c
=
number of sensors in D
c
D
c

,
where D
c
 is the area of D
c
.
Theorem 3.Assume the sensor density at the center of the monitored region
A is ρ
c
.To guarantee the number of the neighbors of the sensors’ close to the
borders be equal to the number of the neighbors of the sensors at the center,for a
point p whose distance to the border of A is r,the sensor density at p should be
ρ
p
=
4πR
2
s
4(π −arccos
r
2R
s
)R
2
s
+r
4R
2
s
−r
2
ρ
c
where R
s
is the sensing range of a sensor.
Proof.Assume the sensor density in a disk is uniform.As shown in Fig.1,D
c
is the disk centered at c (center of the monitored region) with radius of 2R
s
and D
p
is the disk centered at p with radius of 2R
s
minus area A.Since we
assume the transmission range of a sensor is at least twice of the sensing range
of a sensor to guarantee connectivity,the neighbors of the sensor located at c
must be within D
c
.We desire that the number of the neighbors of the sensor
located at c is the same as that of the sensor located at p.This indicates that
the sensor density in D
p
and the sensor density in D
c
satisfy the following
Sensor Scheduling for kCoverage in Wireless Sensor Networks 275
Fig.1.Density computation
condition:ρ
p
=
D
c

D
p

ρ
c
.We know D
c
 = π(2R
s
)
2
and D
p
 = A
1
+ 2A
2
=
π(2R
s
)
2
2π−2α
2π
+ 2(
1
2
r
(2R
s
)
2
−r
2
) = 4(π − α)R
2
s
+ r
4R
2
s
−r
2
,where A
1
is the area ﬁlled with dashed lines,A
2
is the area ﬁlled with dotted lines and
α = arccos
r
2R
s
.Hence,ρ
p
=
4πR
2
s
4(π−arccos
r
2R
s
)R
2
s
+r
√
4R
2
s
−r
2
ρ
c
.
Based on Theorem3,users can develop a plan for deploying sensors such that
any point in the monitored region may be covered by almost the same number
of sensors.This scheme can reduce the number of unallocated sensors.In other
words,the amount of wasted recourse can be minimized and the network lifetime
can be further extended.
6 Simulation Results
In this section,we evaluate GS’s performance by conducting simulations to mea
sure the network lifetime in terms of evaluating the constructed subsets,the
number of unallocated sensors,and the eﬀect of density control mentioned in
Theorem 3.Networks are randomly generated in a ﬁxed region of 100 × 100.
We assume the sensing area of a sensor is circular.Each set of experiments are
conducted for k = 1,2 and 4.All data are averages from 50 times experiments.
6.1 Performance of Greedy Selection
In this section,we study the performance of GS algorithm.The results of our
algorithm are compared with the ideal case which is proved in Theorem 2.
Fig.2(a) shows the comparisons between GS’s results and the ideal results
when the number of sensors varies from 50 to 200 and Density Control is ap
plied.We can see the actual numbers of subsets are close to the ideal results.In
fact,the ratio (actual/ideal) are between 85%and 90%stably.When the sensing
range of the sensors varies from 30 to 80,Fig.2(b) shows that the results of our
algorithm are still very close to the ideal numbers.The ratio tends to be stabi
lized between 80%and 90%.Fig.2(c) shows that our results are almost the same
as the ideal results when Density Control is not applied.Actually the ratios are
all above 90%,whereas it is not good enough.The reason is that the percentage
276 S.Gao,C.T.Vu,and Y.Li
50
100
150
200
0
5
10
15
20
25
30
35
40
45
50
The number of Sensors
The number of subsets
k=1(ideal)
k=1(actual)
k=2(ideal)
k=2(actual)
k=4(ideal)
k=4(actual)
(a) The number of sensors varies
from 50 to 200 with DC
30
40
50
60
70
80
0
5
10
15
20
25
30
Sensors’ Sensing Range
The number of subsets
k=1(ideal)
k=1(actual)
k=2(ideal)
k=2(actual)
k=4(ideal)
k=4(actual)
(b) The sensing range varies
from 30 to 80 with DC
50
100
150
200
0
5
10
15
20
25
30
35
40
45
50
The number of Sensors
The number of Subsets
k=1(ideal)
k=1(actual)
k=2(ideal)
k=2(actual)
k=4(ideal)
k=4(actual)
(c) The number of sensors varies
from 50 to 200 without DC
30
40
50
60
70
80
0
5
10
15
20
25
30
Sensing Range
The number of Subsets
k=1(ideal)
k=1(actual)
k=2(ideal)
k=2(actual)
k=4(ideal)
k=4(actual)
(d) The sensing range varies
from 30 to 80 without DC
Fig.2.Compare GS’s results with the ideal results
of the used sensors is quite low,only 61.34% on average.Due to low usage per
centage,there are enough redundant sensors for constructing more subsets.By
applying Density Control,the usage percentage is improved to 83.17% on aver
age.There are less redundant sensors (potential unallocated sensors) left.The
comparison when increasing sensors’ sensing range without Density Control is
shown in Fig.2(d).All these results show that GS’s results are stable and very
close to the ideal results whatever changing the number of sensors or the sensors’
sensing range.
6.2 Eﬀect of Total Number of Sensors on Network Lifetime
The purpose of this set of simulations is to evaluate how the total number of
deployed sensors aﬀects the network lifetime.The sensing range of a sensor is
set to 50.
Fig.3(a) shows how many subsets can be constructed when the number of
sensors ranges from 50 to 200.As shown in Fig.3(a),the number of the con
structed subsets increases linearly with respect to the network size.This fact is
also validated by Theorem 2.It is shown in Fig.3(b) that the number of nodes
per subset keeps constant and this also consolidates with Fig.3(a).As the cov
erage level k increases,the number of the constructed subsets decreases since
more sensors are required for a subset.
Fig.3(c) illustrates the number of the unallocated sensors.Around 33%∼40%
sensors are not allocated on average.After studying the experiment data,we
Sensor Scheduling for kCoverage in Wireless Sensor Networks 277
50
100
150
200
0
5
10
15
20
25
30
35
40
45
50
The number of Sensors
The number of Subsets
k=1 (no dc)
k=2 (no dc)
k=4 (no dc)
(a) The number of subsets
50
100
150
200
0
5
10
15
20
25
30
The number of Sensors
The number of Sensors per Subset
k=1 (no dc)
k=2 (no dc)
k=4 (no dc)
(b) The number of sensors per
subset
50
100
150
200
0
10
20
30
40
50
60
70
80
The number of Sensors
The number of Unallocated Sensors
k=1 (no dc)
k=2 (no dc)
k=4 (no dc)
(c) The number of unallocated
sensors
30
40
50
60
70
80
0
5
10
15
20
25
30
Sensing Range
The number of Subsets
k=1 (no dc)
k=2 (no dc)
k=4 (no dc)
(d) The number of subsets
30
40
50
60
70
80
0
5
10
15
20
25
30
35
40
45
50
Sensing Range
The number of Sensors per Subset
k=1 (no dc)
k=2 (no dc)
k=4 (no dc)
(e) The number of sensors per
subset
30
40
50
60
70
80
0
10
20
30
40
50
60
70
80
Sensing Range
The number of Unallocated Sensors
k=1 (no dc)
k=2 (no dc)
k=4 (no dc)
(f) The number of unallocated
sensors
Fig.3.Eﬀect of total number of sensors and the sensing range on the network lifetime.
Density Control is NOT applied.
found that only a few small areas close to the corners of the region are not
covered by these unallocated sensors.The reason is that the density of sensors
close to the center of the region is larger than the one close to the corners and
borders.Therefore,there are not enough sensors near the borders to form some
subsets with the sensors at the center of the region.To solve this problem,we
can reduce the number of unallocated sensors through density control which will
be evaluated in section 6.4.
6.3 Eﬀect of Sensing Range on Network Lifetime
The purpose of this set of simulations is to evaluate how the sensing range
of a sensor aﬀects the network lifetime.50 sensors are deployed in the region.
278 S.Gao,C.T.Vu,and Y.Li
0
20
40
60
80
100
0
10
20
30
40
50
60
70
80
90
100
Deploy sensors with DC
0
20
40
60
80
100
0
10
20
30
40
50
60
70
80
90
100
Deploy sensors without DC
sensor
Fig.4.Deploy sensors with and without DC
The sensing range ranges from 30 to 80.Fig.3(d) shows that more subsets are
constructed as the sensing range increases.Even one sensor can cover the whole
area when the sensing range becomes very large.However,only those placed at
the center of the region can solely kcover the entire region except that the sensors
have very large sensing range.Those sensors close to the corners and borders
need other sensors’ cooperation to kcover the whole region.Thus,the curves of
the number of subsets do not keep increasing.There is the maximum number
of subsets which is shown in Theorem 2.Fig.3(e) indicates that larger sensing
range leads to fewer sensors in each subset.Larger sensing range also makes more
sensors at the center of the region be used.In the previous simulation,they are
unallocated sensors generally.With larger sensing range,they can provide the
required coverage level without the help from the sensors close to the corners
and borders.Fig.3(f) validates this fact.On average,39.27% sensors are not
allocated into any subset.
6.4 Eﬀect of Density Control on Network Lifetime
In this set of experiments,we apply Density Control (DC) for sensor deployment
and evaluate its eﬀectiveness.When deploy the sensors,we apply Theorem 3 to
control the density of sensors in the monitored region.By employing DC,we
can deploy more sensors in the areas close to the corners and borders such that
all the sensors have almost the same number of neighbors.In other words,the
monitored region is covered uniformly.The eﬀect of DC is presented in Fig.4.
Due to the space limitation,only the numerical results are shown as following.
In the simulations on increasing the number of sensors from 50 to 200,we ob
served that compared with the cases where DC is not applied,by employing
DC,up to 74.6% (averagely 39.8%) more subsets can be constructed and there
are up to 66% (averagely 60.6%) less unallocated sensors.In the simulations
on increasing the sensing range from 30 to 80,compared with the cases where
DC is not applied,by employing DC,we can obtain 39.68% more subsets on
average and the number of the unallocated sensors is reduced 18.91% on av
erage.Therefore,by deploying sensors more rationally,sensors are used more
eﬀectively.
Sensor Scheduling for kCoverage in Wireless Sensor Networks 279
7 Conclusion and Future Work
In this paper,we investigate a new SSC problemof scheduling sensors to provide
kcoverage for a monitored region with the purpose of maximizing the network
lifetime.We propose a heuristic algorithmto solve the SSC problem.In addition,
we develop a guideline for users to better design a sensor deployment plan by
employing density control.Theoretical analyses as well as simulation results are
presented to evaluate our proposed algorithm.
We will further investigate the kcoverage scheduling problem with more
constraints,such as connectivity,adjustable sensing range and communication
range,bandwidth limitation,transmission delay requirement and etc.In addi
tion,other nongreedy heuristics as well as distributed algorithms are also of our
interest.
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