Wireless Sensor Network, 2011, 3, 189-197
doi:10.4236/wsn.2011.36022 Published Online June 2011 (http://www.SciRP.org/journal/wsn)
Copyright © 2011 SciRes. WSN
LDM (Layered Deployment Model): A Novel Framework
to Deploy Sensors in an Irregular Terrain
Chandan Kumar Bhattacharyya1, Swapan Bhattacharya2
1Department of Computer Science & Engineering, Techno India, Salt Lake, Kolkata, India
2Department of Computer Science & Engineering, Jadavpur University, Kolkata, India
E-mail: ckbckb2010@rediffmail.com, bswapan2000@yahoo.co.in
Received May 1, 2011; revised June 2, 2011; accepted June 8, 2011
Deployment of sensors in any irregular terrain with 100% coverage and connectivity is a challenging issue in
the field of Wireless Sensor Networks. Traditional deployments often assume homogeneous environments,
which ignore the effect of terrain profile as well as the in-network obstacles situated randomly like buildings,
trees, roads and so on. Proper deployment of sensors in such irregular region and its corresponding routing is
one of the most fundamental challenges of Wireless Sensor Networks. In this work, we have considered that
the terrain is irregular in shape and there may be obstacles within the terrain in any random position with any
random shape, which is the reality in real world. With this novel framework, we have shown that an opti-
mum deployment can be achieved in such irregular terrain without compromising coverage as well as con-
nectivity between the sensor nodes for effective routing.
Keywords: Wireless Sensor Networks, Sensor Deployment, Shortest Path, Routing, Irregular Terrain
1. Introduction
The sensor networks are the distributed collection of
sensors (nodes), mobile or localized, with sensing, com-
putation and co mmunication capabilities with in a desired
level of accuracy. Each node needs to know the identity
and location of its neighbors to support processing and
collaboration of information. In addition to the knowl-
edge of topology, each sensor also needs to know its own
location. Due to cost restrictions and to achieve the
maximum life-time by energy savings, these sensor
nodes are rather low-capability devices equipped just
with a simple processing unit and a small radio device
that can sense object and communicate information be-
tween neighbor nodes on ly. In most of the previous work
[1-5], the sensing terrain was considered as regular in
shape and the deployments are movement-assisted with-
out the knowledge of location information. But, if the
terrain is not a regular, which happens actually in real
scenario, we must be very careful about deployment of
nodes as because, the terrain boundary may be the border
of a state or a country and one deployment beyond bor-
der means wastages of resources as well as facing in-
ter-country or inter-state network hazards. In our pro-
posed system, we have considered the terrain as any ran-
dom geometric shape in nature with random obstacles at
random positions within th e terrain as shown in Figure 1.
Our objective is to deploy the sensors only in the Area of
Interest (AoI) marked as yellow skip-ping the pockets
(P1, P2, P3, P4) and obstacles (H1, H2) with optimum
number of nodes without compromising the coverage as
well as connectivity. Pockets, as we define, are the area
outside the AoI but inside its edged-boundary and obsta-
cles are the areas inside the given irregular terrain but
outside the AoI as shown in the Figure 1. The rest of the
paper is organized as follows: In section 2, some pre-
liminaries and assumptions are discussed. The definition
of the problem is proposed and formulated in section 3.
Figure 1. Effective AoI multiple pockets (P1, P2, P3, P4) and
obstacles (H1, H2).
In section 4, we briefly discuss the related work. Section
5 and 6 is our proposal for the topology of node deploy-
ment in LDM framework and corresponding routing
methodology respectively. A simulated study of this so-
lution is given in section 7. Finally, we conclude in sec-
tion 8.
2. Preliminaries and Assumptions
The proper sensing of any object by a sensor is highly
related with the geometric distance of the object from the
sensor. Here we assume that a sensor can sense the en-
ergy emitted by the object in a homogeneous circular
area with maximum radius r, as shown in Figure 2, un-
der the constraint of noise and other distortions. This
energy is called Threshold Energy (Eth) and an object
will not be sensed if the received energy by the sensor is
less than this threshold energy. This coverage is consid-
ered as optimum coverage of a sensor with desired level
of acceptable value. Assuming the energy emitted by an
object is constant, the signal energy Es, as detected by
sensor si for an object situated at distance dt from the
sensor will be, Es = E0(1-αdn) where E0 is the energy at
distance 0 i.e. maximum energy, α is the decay
co-efficient and dn is the normalized distance of the ob-
ject from the sensor and will be expressed as dn = dt/r
where r is the optimum sensing range. For example, in
the Figure 2, the signal energies for three different loca-
tions ar e expressed as:
Eth = E0(1 α) = Threshold Energy;
Ex = E0(1 – αdx/r) = Energy at distance dx;
Ey = E0(1 αdy/r) = Energy at distance dy.
Since dx > dy, it is obviously Ex < Ey. An object will be
sensed only if its emitted energy lies between E0 and Eth.
We assume that the wireless sensor nodes are given as a
set S with n sensor nodes where 1jni and for
each sensor si, its location iii
is known as it is
deployed. We also assume that all the sensors are static
sensors and there are no road constraints within AoI.
Each sensor is assumed to have same sensing range as
Figure 2. Measurement of signal energy with respect to the
denoted by r. A pair of sensors will be able to see (cov-
erage) and hear (connectivity) each other if they have
overlapped coverage space. If only coverage is consid-
ered, less number of nodes will be required but the de-
ployed nodes will not be able to communicate with each
other. Figure 3 shows the relation between the optimal
coverage and connectivity. As we move from coverage
to connectivity, the overlapping domain (d) gets in-
creased where
. Here, we assume homoge-
neous coverage and connectivity i.e. both coverage and
connectivity ranges are same and is equal to r.
3. Problem Definition and Objectives
To communicate between each other with optimum cov-
erage we have to deploy the next node at the maximum
sensing boundary with threshold signal energy Eth to any
of the four sides (i.e. Right, Left, Up, Down) of the pre-
viously deployed. To minimize the channel overhead, we
have proposed the concept of layered accumulation i.e.
outer layer information will only be transmitted to its
immediate inner layer and not directly to Fusion Node
and communication to Fusion Node will be done only
through First layer nodes (and/or from the boundary
nodes for leaving of any object from AoI). Since volume
of information is being increased layer by layer towards
the Fusion Node, we have deployed nodes with variable
capacities in different layers. We define capacity of a
node as its rate of consumption of power, maximum sto-
rage/buffer size, processing speed etc. Hence, the objec-
tive or the pr oblem definition of our proposed model can
be defined as:
Finding Fusion Node Capacity
Deploying Layer wise Sensors with variable capaci-
Designing Effective Routing Model
4. Related Work
Several deployment schemes with existing holes [7-9] in
the network have been proposed to enhance the coverage.
They have considered that the target region is regular and
rectangular and the holes are situated randomly within
Figure 3. Moving from coverage to connectivity.
Copyright © 2011 SciRes. WSN
Copyright © 2011 SciRes. WSN
Table 1. Comparative analysis of existing work with proposed model.
Studies Coverage Density Full
Coverage Boundary In-boundary
Obstacle Obstacle
Knowledge of
Location Shortest P ath
[10] Non-UniformNo Irregular Not Exist Not KnownNo Not KnownNot Known
[11] Non-UniformNo Irregular Not Exist Not KnownNo Not KnownNot Known
[12] Non-UniformNo Irregular Not Exist Not KnownNo Not KnownNot Known
[13] Uniform Yes Irregular Not Exist Not KnownNo Not KnownNot Known
[14] Non-UniformNo Irregular Not Exist Not KnownNo Not KnownNot Known
[15] Non-UniformNo Irregular Not Exist Not KnownNo Not KnownNot Known
(Proposed) Uniform Yes Irregular Exist and
Irregular Not KnownYes Known Known
5. Proposed Model the target boundary. More over the geometry of the ho les
are also bounded and ar e defined as a regular graph with
certain number of nodes and edges. In certain cases,
holes defined with less than four edges could turn out to
be large areas that act as greater barriers to the network
than normal. An extreme scenario could present itself
with the occurrence of a large area that is only connected
through two edges. With such consideration, we need to
deploy more nodes to cover the entire range of area,
which is a trade-off with cost optimization. In [10-15],
irregular areas have been considered with no obstacles. A
comparative analysis is shown in Table 1 with proposed
Let us define our proposed model i.e. Layered Deploy-
ment Model (LDM). If a logical grid is created around a
deployed node, some part of the grid area remains un-
covered as shown in the Figure 4. The uncovered area
will further be covered with next layer of deployment at
distance r from the deployed node at right, left, up and
down subject to the calculated co-ordinates of deploy-
ment lie within AoI, otherwise we have to search for next
effective location in any of the four sides at distance r
and establish connectivity. The stepwise deployment of
five nodes is shown in the Figure 5 and corresponding
maximum coverage area with optimum connectivity is
shown in the Figure 6. Figure 7 shows the final model
The accuracy of sensor placement may be subject to
various errors. Kenan Xu, et al. [16], in their paper, iden-
tified two deployment errors namely, misalignment and
random errors. They derived the minimum number of
sensors required by a robust grid-based sensor deploy-
ment assuming that the errors are bounded. F. Zhao, et al.
[17], have addressed the dynamic sensor collaboration
problem to determine dynamically which sensor is most
appropriate to perform the sensing, what needs to be
sensed, and to whom to communicate the information. It
is based on the information-driven sensor querying ap-
proach, enabling collaboration, under resource con-
straints and cost of transmitting information. Here, the
next node selection is done by predicting Mahalanobis
distance measure technique where the computation from
predicted likelihood function may be strongly biased by
the prior distribution. Y. Rachlin, R. Negi, and P. Khosla,
[18] have addressed the technique of measuring sensing
capacity in a sensor network with respect to the maxi-
mum ratio of target positions to sensors as achievable
within a certain tolerable distortion. As one target is be-
ing sensed by more than one sensor, the network will
soon get flooded with redundant information. Moreover,
sensors lifetime will eventually get reduced as all the
time more than one sensor is sensing one target. [19,20]
[21] are based on grid-based Stable Routing Protocol
with multi-hop broadcast technique. In [22] several
power-efficient routing algorithms are proposed for a
sensor network with 2D gri d top olo gy .
Figure 4. Logical grid with covered and uncovered area for
a node deployed.
Figure 5. Stepwise deployment of five nodes (one central
and four neighbors) at right, le ft, up and down respectively.
Figure 6. Final view of optimum connectivity (yellow line)
and maximum coverage area (blue line) with five nodes
Figure 7. Layer 0 and layer 1 deployment within AoI with
maximum coverage area (8r2) with connectivit y.
of lay ered deployment with two layers and the relation
between layer number and coverage area with total de-
ployed node is shown in Table 2.
In case of existing obstacles, the deployment will be
done to the next effective location that lies within AoI
and in consequence, connectivity will be rebuilt accord-
ingly. To find the deployment co-ordinates, we first
make the boundary of the irregular space by squaring the
boundary of the sensing terrain as shown in the Figure 1.
Table 2. Layerwise node de ployment.
Range of Node
Node 01 00 2r2
4 5 01 - 04 8r2
8 13 05 - 12 18r2
12 25 13 - 24 32r2
16 41 25 - 40 50r2
4l 2l2 + 2l + 1(2l2–2l+1) -
(2l2+2l) 2(l + 1)2r2
Nodes are deployed from the center of the regular boun-
dary as its co-ordinate is known and the first node will be
the Fusion Node i.e. the Central Server. We deploy the
first node i.e. Fusion Node at the center of the square
boundary of the terrain to reduce the average hop be-
tween any node and the Fusion Node provided the center
lies within AoI and not within any obstacle. However,
depending the complexity of the terrain property, the
Central Server can also be placed at any desired location
from which other nodes will be deployed. We assume
that the entire sensing area has no geographic limitation
to deploy or access any node unless it lies in obstacles
where nodes will not be deployed at all.
5.1. Average Capacity of Fusion Node
As the volume of data aggregation to the Fusion Node is
directly proportionate to the hop size i.e. layer number,
the capacity of the Fusion Node controls the size of the
network. We are assuming that one Fusion Node is re-
sponsible for data ag gregation of a single network. For a
large space where one Fusion Node will not be able to
cover the entire network we have to partition the network
into sub-networks each of which will be headed by one
sub-Fusion Node. Then we have to build the network of
sub-Fusion Nodes to cover the entire area.
Let m = maximum message in bits (including its own
address, number, tracking time of object etc) a node is
sending to Fusion Centre. Let hmax = maximum
hop-distance from a boundary node (sender node) to the
Fusion Centre and Let β = the bit size that every node is
padding with the message for update information. So, the
dynamic information created by nodes (intermediate
node address, number, time-stamp etc) in bits, as denoted
by md = (hmax – 1)β and the maximum message size that
will reach to Fusion Node = mmax = md + m. Let B be the
maximum buffer-size of a node, so, the message will
be split to p no. of packets where p = mmax /B. If pk be
the packet header size, and pm be the message size (= B
for maximum), the minimum capacity of a Fusion Node
should be p(pk + pm) bits to receive the in-bound infor-
mation from different nodes. For in network data aggre-
gation, more space is also required for Fusion Node and
the processing element of Fusion Node should also be
very powerful.
5.2. Deployment of Fusion Node
Since the pockets or obstacles may lie in any random
position, the co-ordinate of Fusion Node may lie in any
of the following three positions as stated below and is
shown in the Figure 8:
Withi n AoI
Copyright © 2011 SciRes. WSN
Figure 8. (a) center within AoI with odd number of inter-
section (b) center within pocket with even number of inter-
section (c) center within obstacle with even number of in-
Within any pocket
Within any obstacle
We will skip deploying Fusion Node at center except
the first condition and keep on searching for the next
accepted location within AoI in any of the four sides i.e.
Right, Left, Up and Down. To test whether the derived
co-ordinate lies within AoI or not, we have counted the
number of intersection points from the Fusion Node
co-ordinate to the boundary as shown in Figure 10. It is
obvious that if the number of intersection is odd (1,
3, 5, ), the point lies within AoI, otherwise (0 or
even), it is outside AoI i.e. it may fall either in pocket or
in obstacle. The algorithm for Fusion Deploy is stated
Algorithm for Fusion Node Deployment within AoI
FusionNodeDeploy() {
Find boundary co-ordinates of top-left
tl tl
y and
rb rb
Find center co-ordinate ,
tl rbtlrb
xx yy 
Figure 9. Fusion Node (layer 0) and other nodes in Layer 1,
2 and 3 (Node Number, Layer) as shown in different color
in AoI assuming no obstacle. The connectivity is shown in
Figure 10. Automatic bypassing of deployment within hole
by intersection count method.
5.3. Deployment of Other Nodes
If (LieAOI()) {
StoreCoordinate(); }
Else {
While (!LieAOI())
TestRight(); TestLeft(); TestUp(); TestDown();
StoreCoordinate(); } }
Once the Fusion Node has been deployed, we will de-
ploy other nodes to cover the entire sensing space within
AoI in layer by layer as shown in the Figure 9. For ho-
mogeneous distribution of the nodes in layer and for bet-
ter connectivity, we will deploy nodes in Right, Left, Up
and Down order so that any node will have the informa-
tion about its next four neighbor nodes along its layer
number [23]. For the deployment of next node in any of
the side we consider the intersection number for bypass-
ing the deployment within obstacle and reserve the sen-
sor id in order. The algorithm for deployment to right is
shown below and its corresponding operation is depicted
in Figure 10.
Copyright © 2011 SciRes. WSN
Algorithm for Fusion Node Deployment within AoI
count = 0;
GetNodeRight(si) {
while (!boundary()) {
if (intersection(si, si+1)) {
if (odd(count)) CurrentNodeId = si;
if(even(count)) si = CurrentNodeId;
if (even(count) {
GetNodeRight(si+1) }
else GetNodeRight(si+1); } }
5.4. Deployment Exception
According to the algorithm for node deployment, the
nodes are being deployed as per Figure 9 where we
count the number of intersection(s). However, when the
intersection line touches the boundary without crossin g it,
as shown in the Figure 11, it senses as odd count and
skip deploying nodes, which creates algorithmic de-
ployment error. The nature of error is in random and the
probability of the occurrence of such error is very negli-
gible and highly depends on the shape of the area and the
radius of the coverage of the deployed node. We have
handled this type of exceptions by finding the direction
of the movement of curve during the scanning of the
pixels with its adjacent upper and lower pixels as shown
in Figure 12. As we are scanning lines horizontally, the
upper pixels from the central one (as per Figure 12(a)
determine the upward movement of the curve, and the
lower pixels determine the downwards movement of the
curve. Following conditions satisfies whether the cut is
an intersection or a touch:
If the curve has both upwards and downwards move-
ment, it is an intersection (as per Figure 12(b)).
If the curve has either upward or downward move-
ment, it is touch (as per Figure 12(c)).
Figure 11. Deployme nt exception.
Figure 12. Analysis of deployment exception.
If the curve has no movement, it is either a point or a
line parallel to the scanning line. (as per Figure
5.5. Performance of Algorithm
For a worst-case scenario with native assumptions, let us
consider the terrain, as rectangular shape having width, w
and height, h and it is free from any obstacle. Let the
nodes are deployed within the terrain in interval of r. we
also assume that all nodes are homogeneous. Number of
nodes required to cover each row in interval 1rwr
and each column = 1hr
. So maximum total number
nodes required to cover the entire region =
. To find obstacle boundary or Terrain boundary
to deploy the nodes, intersection scan per row in interval
r will be
1rw rwr
 since we have to con-
sider two extreme boundaries. So, the complexity will
 
w rdrrd  where1hr
6. Connectivity and Routing
According to the proposed model of layered-deployment,
the logical covered area for the deployment of nodes is
shown in the Figure 9 (in three layers with no obstacle)
and corresponding relation of layer with deployed nodes
is shown in the Table 2. Layer numbers are increasing
from Fusion Node to boundary node in step one. A node
with layer number l can maintain a hop table that con-
tains the connected node(s) situated at layer number l-1.
Similarly, nodes in layer l-1 hold the connected node(s)
situated in layer l-2, nodes in layer l-2 hold the connected
node(s) situated in layer l-3, and so on and finally we can
reach to Fusion Node (with layer 0) through the con-
nected nodes that are situated in layer 1. Hence, it is clear
that from any node at any layer a complete connected
path towards the Fusion Node can be established which
will obviously be the shortest path from that node to the
Copyright © 2011 SciRes. WSN
Fusion Node. The complete shortest path history from
any node to the Central Server as per Figure 9 is shown
in Table 3.
Since the nodes are connected with known co-ordinate
as well as with known neighbors, more than one shortest
path can be generated and the entire path can be stored in
the node database so that for any crisis in any selected
path, an alternative path can also be taken instantly.
Since all the shortest path history is already kept with
each deployed node during its deployment, no run-time
searching of alternative shortest path is required for each
link failure, which eventually saves huge amount of
run-time shortest path searching time which is a chal-
lenging problem for most of the major previous works.
7. Simulation
It is obvious that the cost of deployment is proportionate
to the sensing range of each node. With greater range,
the number of deployed nodes will be minimized but at
the same time, it also increases the boundary wastage.
Therefore, the optimum deployment will definitely be a
challenge and can only be approximated with different
simulated result. we have tested with different r value
and find the optimum topology with respect to the boun-
dary wastage. We have taken three different random ir-
regular sensing terrain with variable obstacles as shown
in Figure 13 and find the optimum topology (as per
Figure 14) with minimum wastages and with full cover-
age and co nn ectiv ity. Figure 15 shows different situ atio n
Table 3. Shortest path history.
Node Layer
No. R L U D
Path Thru
Hop Table
0 0 1 2 3 4 -
1 5 0 6 7 1-0
2 0 8 9 10 2-0
3 6 9 11 0 3-0
7 10 0 12 4-0
5 13 1 14 15 5-1-0
6 14 3 16 1
15 4 1 17 7-1-0
… … … … … … …
13 N 5 N N 13-5-1-0
14 N 6 N 5
N 7 5 N 15-5-1-0
… … … … … … …
Figure 13. Three different shape of random geometric area.
Figure 14. Optimum topology with different shapes: pock-
ets with no obstacle (a), single obstacle (b), multiple obstacle
Copyright © 2011 SciRes. WSN
Figure 15. Pair {Total deploy node, covering range}ed ratio
for shapes A, B and C as per Figure 13.
Figure 16. Scree nshot of deploy ment with layer (in differe n
f deployment with the variation of r in pair {sensing
this paper, we have introduced the model of lay
deployment of wireless sensors with corresponding
shortest-path routing technique in any random irregular
color) corresponding to 13(b).
radius, total node}. A partial node database as per Figure
16 is shown in Table 4.
8. Conclusions
Table 4. Node database corresponding to 13(b).
Node IdLayer
No Left
Node Right
Node Up
Node Down
0 0 NULL 1 2 3
0 2
3 1 NULL 6 0 22
4 2 1 7 8 9
5 2 2 8 ULL1
6 2 3 9 1 23
7 3 4 10 11 12
8 3 5 11 NULL 4
9 3 6 12 4 24
10 4 7 13 14 15
… … … … … …
… … … … … …
geohic a The uni featuas ach
with this co-ordinated red deyment are:
Average hop-count is minimum as Sink is terrain-
about its
ighbour addresses of each node are known
d with all possible shortest
well detected as one of its
] L. Zhao and Q. L. Liang, “Fuzzy Deployment for Wire-
etworks,” Proceedings of the 2005 IEEE
onference on Computational Intelligence
grap rea.major queres ieved
laye plo
At the time of deployment, nodes are aware
all four neighbours with Ids
All the ne
The shortest path to Sink is also known to each node
at its time of deployment
Topology can be redefined with the variation of indi
vidual sensing range
Instant routing is achieve
Boundary nodes are
neighbour will be NULL
9. References
[1 less Sensor N
International C
for Homeland Security and Personal Safety, Orlando,
2005, pp. 79-83. doi:10.1109/CIHSPS.2005.1500615
[2] Y. C. Wang, C. C. Hu and Y. C. Tseng, “Efficient De-
ployment Algorithms for Ensuring Coverage and Con-
nectivity of Wireless Sensor Networks,” Proceedings of
First International Conference on Wireless Internet, Bu-
dapest, 2005, pp. 114-121. doi:10.1109/WICON.2005.13
[3] G. Wang, G. Cao and T. L. Porta, “Movement-Assisted
Sensor Deployment,” IEEE Transactions on Mobile
Computing, Vol. 5, No. 6, 2006, pp. 640-652.
[4] S. H. Yang, M. L. Li and J. Wu, “Scan-Based Movement-
Assisted Sensor Deployment Methods in Wire
Networks,” Proceedings of
less Sensor
Parallel and Distributed Sys-
tems, IEEE Transactions Publication, Vol. 18, No. 8,
2007, pp. 1108-1121.
[5] C. Fang and C. P. Low, “Unified Framework for Move-
Copyright © 2011 SciRes. WSN
Copyright © 2011 SciRes. WSN
Deployment,” Proceedings of
Networking Conference
6, pp.
ment-Assisted Sensor
Wireless Communications and,
Las Vegas, 31 March-3 April 2008, pp. 2057-2062.
[6] M. de Berg, M. van Kreveld, M. Overmars and O.
Schwarzkopf, “Computational Geometry, Algorithm and
Application,” 2nd Edition, Springer, Berlin, 2000.
[7] Q. Fang, J. Gao and L. J. Guibas, “Locating and Bypass-
ing Holes in Sensor Networks,” Proceedings of Mobile
Networks and Applications, Vol. 11, No. 2, 200
187-200. doi:10.1007/s11036-006-4471-y
[8] F. Reitsma and S. Engel, “Searching for 2D Spatial Net-
work Holes,” Proceedings of International Conference on
Computational Science and Its Applications, Assisi, 14-
Computational Geometry,
International Conference on
17 May 2004, pp. 1069-1078.
[9] S. Funke and C. Klein, “Hole Detection or: How much
Geometry Hides in Connectivity?” Proceedings of the
22nd Annual Symposium on
Sedona, 2006, pp. 377-385.
[10] B. D. Ying and Z. Z. Hou, “Irregular-Location Based Key
Pre-Distribution Scheme for Distribution Sensor Net-
works,” Proceedings of 1st
Information Science and Engineering, Nanjing, 26-28
December 2009, pp. 4042-4046.
[11] B. Xiao, L. Chen, Q. J. Xiao and M. L. Li, “Reliable An-
chor-Based Sensor Localization in Irr
Transactions on Mobile Comp
egular Areas,” IEEE
uting, Vol. 9, No. 1, 2010,
Proceedings of World Congress on Nature &
ional Conference on Com-
Takahara and H. Hassanein, “On the Ro-
iven Dy-
pp. 60-72.
[12] S. K. Udgata, S. L. Sabat and S. Mini, “Sensor Deploy-
ment in Irregular Terrain Using Artificial Bee Colony
Biologically Inspired Computing, Coimbatore, 9-11 De-
cember 2009, pp. 1309-1314.
[13] G. Takahara, K. Xu and H. Hassanein, “Efficient Cover-
age Planning for Grid-Based Wireless Sensor Networks,”
Proceedings of IEEE Internat
munications, Glasgow, 24-28 June 2007, pp. 3522-3526.
[14] C. Y. Chang, C. T. Chang, Y. C. Chen and H. R. Chang,
“Obstacle-Resistant Deployment Algorithms for Wireless
Sensor Networks,” IEEE Transactions on Vehicular
Technology, Vol. 58, No. 6, 2009, pp. 2925- 2941.
[15] T. L. Chin, “Sensor Deployment for Collaborative
Detection in the Presence of Obstacles,” Proceedings of
IEEE Global Telecommunications Conference, Hawaii,
2009, pp. 1-5.
[16] K. N. Xu, G.
bustness of Grid-Based Deployment in Wireless Sensor
Networks,” Proceedings of the 2006 International Con-
ference on Wireless Communications and Mobile Com-
puting, British Columbia, 2006, pp. 1183-1188.
[17] F. Zhao, J. Shin and J. Reich, “Information-Dr
namic Sensor Collaboration for Tracking Applications,”
Signal Processing Magazine, Vol. 19, No. 2, 2002, pp.
61-72. doi:10.1109/79.985685
[18] Y. Rachlin, R. Negi and P. Khosla, “Sensing Capacity for
, “Sensor Deployment Strat-
Target Detection,” Information Theory Workshop, 24-29
October 2004, pp. 147-152.
[19] Z. H. Yuan and G. F. Wang
egy for Collaborative Target Detection with Guaranteed
Accuracy,” Proceedings of the 4th International Confer-
ence on Mobile Ad-hoc and Sensor Networks, Wuhan,
10-12 December 2008, pp. 68-71.
[20] Z. Y. Wu, H. T. Song, S. F. Jiang and X. M. Xu, “A
i, “Coverage-Preserving Routing Protocols for
Grid-Based Stable Routing Algorithm in Mobile Ad Hoc
Networks,” First Asia International Conference on Mod-
elling & Simulation, Phuket, 27-30 March 2007, pp.
[21] Y. R. Tsa
Randomly Distributed Wireless Sensor Networks,” IEEE
Transactions on Wireless Communications, Vol. 6, No. 4,
2007, pp. 1240-1245. doi:10.1109/TWC.2007.348320
[22] J. Zhang and H. Shi, “Energy-Efficient Routing for 2D
Grid Wireless Sensor Networks,” Proceedings of Inter-
national Conference on Information Technology: Re-
search and Education, 11-13 August 2003, pp. 311-315.
[23] C. Kr. Bhattacharyya and S. Bhattacharyya, “Neighbor-
Assisted Sensor Deployment in an Irregular Space: A
Unified Framework,” Proceedings of the 15th Asia-
Pacific IEEE International Conference on Communica-
tions, Shanghai, 8-10 October 2009, pp. 834-837.