The document summarizes a cell-based clustering algorithm proposed for large wireless sensor networks to reduce energy consumption. The key points are: 1. The target field is divided into small hexagonal cells, with sensor nodes in each cell forming a cluster. 2. A low-overhead algorithm is presented for electing cluster heads within each cell based on node energy levels. 3. An optimal inter-cluster routing algorithm is also proposed to establish communication between adjacent cell clusters using the fewest hops. 4. The performance of the cell-based clustering algorithm is evaluated against the GAF algorithm, showing it generates approximately the same number of clusters but with shorter average inter-cluster path lengths, extending

1. 2010 International Conference on Communications and Mobile Computing
A Cell Based Clustering Algorithm in Large Wireless Sensor Networks
Kezhong Lu1, Zhenghua Zheng2, Lu Xian1, Lin Xiaohui2*
1
College of Computer Science and Software Engineering, Shenzhen University, China
2
College of Information Engineering, Shenzhen University, China
*
Corresponding author email: xhliu@szu.edu.cn
Abstract As observed in field applications, energy
Energy is one of most critical resources in wireless consumption by communication accounts for about
sensor networks. Clustering is an effective method to 70% of the total energy in wireless sensor networks
reduce energy consumption of sensor nodes. In this [5,6]. It’s composed of sending data, receiving data and
paper we propose a cell base clustering algorithm. The idle-listening. Researches have shown that energy
target field is divided into small non-overlapping cells. dissipation of idle-listening can’t be ignored compared
Sensor node set in each cell is a cluster. The size of with energy consumption of sending and receiving data
cell is well selected so that any node in adjacent cell [7,8]. Especially in the application scenarios with
can communicate with each other. We also present a modest traffic, idle-listening completely dominates the
low-overhead cluster head electing algorithm and an whole energy consumption of wireless sensor
optimal inter-clustering routing algorithm. We networks.
evaluate the performance of our proposed clustering Clustering is an effective method to reduce energy
algorithm with comparing to GAF algorithm. The consumption of sensor nodes in large wireless sensor
numbers of clusters generated by the two algorithms networks. Sensor nodes are grouped into clusters in
are approximately equal. But the average length of which a node is designated as cluster head. This
inter-cluster communication path of our proposed hierarchical network has two layers: the lower layer
algorithm is less than GAF algorithm. So the network consists of sensor nodes in each cluster for intra-cluster
lifetime by our proposed algorithm is longer. communication, and the upper layer consists of cluster
heads for inter-cluster communication [9]. The upper
Key words: wireless sensor network; clustering; layer is called as backbone network whose task is to
energy efficiency; network lifetime; cell relay data between two clusters. Sensor node which
isn’t in the backbone network can put its radio into
1. Introduction sleep mode when idle to save energy. Besides cluster
Recently, wireless sensor networks composed of head can aggregate data from sensor nodes in the
large numbers of cheap sensor nodes are more and cluster to reduce communication traffic.
more widely used in fields such as environmental The questions of clustering are how to group sensor
monitoring, field survey, traffic monitoring, disaster nodes into clusters and how to select head of each
salvage, target tracking, national defense and military cluster. Because the topology of wireless sensor
[1,2,3,4]. Sensor node which integrates sensing, network is volatile due to death of sensor node,
computing and communicating function can clustering need to be performed repeatedly. Therefore
communicate with each other by wireless radio. As the the overhead of the clustering algorithm should be low.
transmission range of sensor node is short, wireless Local algorithm that each node independently makes
sensor networks are multi-hop network. Sensor node its decisions based on local information is preferred. In
acts as both data generator and data router. this paper we propose a cell based clustering algorithm
Sensor node is typically equipped with a pair of AA (CBC algorithm) in which the target field is partitioned
batteries due to its small size and low cost. And it’s into cells. Sensor nodes in the same cell are grouped
difficult to replace the batteries of sensor node because into a cluster. The sensor node with the maximum
sensor nodes are massive and the sensing field may be energy in the cluster is selected to be cluster head.
dangerous. Consequently wireless sensor networks are The remainder of this paper is organized as follows.
very energy-limited. Many researches have concerned Section 2 reviews the related works. Section 3
of designing protocols to reduce energy consumption describes our proposed cell based clustering algorithm.
and prolong network lifetime. A comparative performance evaluation is presented in
section 4. This paper is concluded in section 5.
978-0-7695-3989-8/10 $26.00 © 2010 IEEE 182
DOI 10.1109/CMC.2010.70
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2. head is re-elected if its current energy level is below
2. Related Works the average value.
There’re many researches about network clustering
to reduce energy consumption and prolong network 3. The Proposed Clustering Algorithm
lifetime in wireless sensor network in recent years. In this section, first network model is given, and
Heinzilman et al. [10] proposed Low-Energy then our proposed cell based clustering algorithm is
Adaptive Clustering Hierarchy (LEACH), which is a described.
self-organizing, adaptive clustering protocol utilizing 3.1. Network Model
randomization to evenly spread work load among Consider a wireless sensor network consisting of a
nodes in the network. In cluster set-up phase, each large number of sensor nodes which is dispersed on a
node elects itself to be a cluster head with a certain rectangular field. Let l and w denote the length and the
probability. Then each non-cluster head node joins a width of the rectangular field respectively. We assume
cluster by choosing the cluster head that requires the the following properties about the sensor network
minimum communication energy. Non-cluster head model:
node can turn off its radio except during its (1) Sensor nodes are evenly distributed in the target
transmitting time. Each cluster head aggregates data field. Once deployed, all sensor nodes are static.
from members and transmits the compressed data to (2) All sensor nodes have same capabilities of
the data sink directly. Since the cluster head may be far sensing, processing and communication.
away from the data sink, it will cost high energy. (3) The transmission range of all sensor nodes is
same and fixed which’s denoted by R. Two sensor
r nodes can communicate with each other if their
distance is less than R.
(4) Each sensor node knows its location information
r which can be provided by GPS or other location
systems.
3.2. Cell Based Clustering Algorithm
r First we discuss how to group sensor nodes into
clusters. Similar to GAF, the target field is divided into
r r r r small non-overlapping “virtual cells” which is a
regular hexagon. Sensor nodes belonging to the same
Figure 1 Example of virtual grid in GAF cell form a cluster. Without loss of generality, we
Xu et al. [11] presented a Geographical Adaptive assume l≥w. To minimize the total number of clusters,
Fidelity (GAF) algorithm. As depicted in figure 1, the we partition the rectangle into cells by way as
whole area where nodes are distributed is divided into illustrated in figure 2. The cells are arranged in array.
small “virtual grids”. Each node uses its location Each cell is identified with a two-tuples (i,j), where i is
information which can be provided by GPS or other the row order of the array and j is the column order of
location systems to determine which grid it belongs to. the array. Let Ci,j denotes the cell whose identification
Nodes belonging to the same grid form a cluster. Each is (i,j). To ensure cluster head can relay data from
node in a cluster has opportunity to be selected as adjacent cell, it’s required that any node in adjacent
cluster head. To ensure cluster head can relay data cell can communicate with each other. The maximum
between clusters, it’s required that any node in adjacent distance between any two nodes in adjacent cell is
grid can communicate with each other. Let R denote marked in figure 2. Let R denote the transmission
the transmission range of sensor node and r denote the range of sensor node and r denote the radius of the
size length of virtual grid. Therefore r≤R/ 5 must be circumcircle of cell. Therefore, we get:
held. r2+(2 3 r)2≤R2 (1)
Moussaoui et al. [12] presented a centralized Then r≤R/ 13 . In fact, we set r=R/ 13 to reduce the
clustering algorithm. Sensor nodes are organized into total number of clusters.
no overlapping clusters by taking into account a
combined effect of the cluster size, transmission power
and energy levels of nodes. Each node can
communicate with any other node in a cluster. Once all
clusters are set up, they don’t change in order to reduce
the computation and communication costs. Cluster
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3. balance energy of each node within cluster, it’s
4,0 4,1 4,2 4,3 4,4 4,5 important to elect the node with the maximum energy
to be cluster head. On the other hand, the energy of
3,0 3,1 3,2 3,3 3,4 3,5 3,6 each node will dynamically decrease as the time
elapses, so the cluster head must be re-elected
u periodically. Here we give a low-cost local algorithm
2,0 2,1 2,2 v 2,3 2,4 2,5 w
for electing cluster head, which is described as follows:
(1) If a node finds there’s no cluster head, it set a
1,0 1,1 1,2 R 1,3 1,4 1,5 1,6
timer which is in inverse proportion to its energy. If no
r cluster head is elected before the timer fires, it elects
0,0 0,1 0,2 0,3 0,4 0,5 itself to be cluster head.
(2) If a node finds its energy is more than twice the
l energy of current cluster head, it elect itself to be new
cluster head replacing current cluster head.
Figure 2 Partitioning the rectangle into virtual
Because each cluster member can directly
cells
communicate with the cluster head, intra-cluster
According to location information, each node can communication is sample. Subsequently we discuss
determine which cell it belongs to without exchanging inter-cluster communication. Assume only adjacent
message with each other. Assume the origin is the left cell can directly communicate with each other due to
down corner of the rectangle, the coordinate of the restriction of MAC protocol. Let (si,sj) and (di,dj)
node is (x,y), the identification of the cell in which the denote the identification of the source cell and the
node is located is (i,j). The value of (i,j) can be destination cell respectively. The question is how to
calculated from (x,y) by the following procedure: establish the communication path connecting Csi,sj and
Procedure Cal_Cell_ID Cdi,dj. As illustrated in figure 2, we first route vertically
Input: x, y, r to the cell which has the same row order as the
Output: i, j destination cell while try to reduce the column
i= ⎣ y / (3 / 2r )⎦ ; difference, then route horizontally to the destination
if (i%2=0) cell. Let Cci,cj denote the current cell and Cni,nj denote
j= ⎣x / ( 3r )⎦ ; the next routing cell. The value of (ni,nj) can be
u=x-j× 3 r; calculated by the following procedure:
else Procedure Route
j= ⎣x / ( )
3 r + 0 .5 ⎦; Input: di, dj, ci, cj
Output: ni, nj
u=x-(j-0.5)× 3 r;
if (di=ci)
v=y-i×3/2r; ni=ci;
if (v>r) if (dj<cj)
v=v-r; nj=cj-1;
if (u< 3 v) else
if (i%2=1) nj=cj+1;
j--; else
i++; if (di<ci)
else if (u> 3 r- 3 v) ni=ci-1;
else
if (i%2=0)
ni=ci+1;
j++;
if (ci%2=1 and dj<cj)
i++;
nj=cj-1;
return (i, j); else if (ci%2=0 and dj>cj)
nj=cj+1;
Figure 3 Procedure of calculating cell else
nj=cj;
identification from coordinate of node
return (ni, nj);
After the clustering procedure, all nodes are
grouped into clusters. Each node belongs to only one Figure 4 Procedure of routing between clusters
cluster. Then a cluster head must be elected from the It’s easy to see that the above routing procedure can
nodes set in each cluster. Cluster head perform more always produce the optimal communication path
functions than non-cluster head nodes and can’t go to between the source cluster and the dentition cluster if
sleep, consequently it will consume more energy. To measured by the hops of the communication path.
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4. ⎡ 5l ⎤ ⎡ 5 w ⎤
4. Performance Evaluation LPGAF= ⎢ ⎥+⎢ ⎥−2 (5)
⎢ R ⎥ ⎢ R ⎥
In this section, we evaluate the performance of our
CBC algorithm with comparing to GAF algorithm For CBC algorithm, if the number of rows is even,
presented in [11]. The measurements include the the identification of the cell at right up corner is
number of clusters, the length of inter-cluster ( ⎡2 w /(3r ) + 1 / 3⎤ -1, ⎡l /( 3r ) + 0.5⎤ -1). Otherwise the
communication path, and the network lifetime. identification is ( ⎡2 w /(3r ) + 1 / 3⎤ -1, ⎡l /( 3r )⎤ -1). So the
First we analyze the number of clusters generated largest length of inter-cluster communication path of
by CBC algorithm and GAF algorithm respectively. CBC algorithm which’s denoted by LPCBC can be
The smaller the number of clusters, the more energy is obtained as follows:
saved because the more nodes can go to sleep. The ⎧⎡ l 1 ⎤ ⎡ 2w 1 ⎤ ⎡ 2w 1 ⎤
number of clusters by GAF algorithm which’s denoted ⎪⎢ + ⎥+⎢ + ⎥ /2−2 ⎢ 3r + 3 ⎥ is even
by CNGAF can be easily obtained as follows: ⎪⎢ 3r 2 ⎥ ⎢ 3r 3 ⎥ ⎢ ⎥
LPCBC= ⎨ ,
⎡ l ⎤ ⎡ w ⎤ ⎡ 5l ⎤ ⎡ 5 w ⎤ ⎪⎡ l ⎤ ⎡ 2w 1 ⎤ 3 ⎡ 2w 1 ⎤
CNGAF= ⎢ ⎥ ⎢ ⎥ = ⎢ ⎥⎢ ⎥ (2) ⎪⎢ ⎥+⎢ + /2− ⎢ 3r + 3 ⎥ is odd
⎢ r ⎥⎢ r ⎥ ⎢ R ⎥⎢ R ⎥ ⎩⎢ 3r ⎥ ⎢ 3r 3 ⎥
⎥ 2 ⎢ ⎥
For CBC algorithm, the cell number of each even where r=R/ 13 (6)
row is ⎡l /( 3r )⎤ , the cell number of each odd row We can compute the asymptotic value of
is ⎡l /( 3r ) + 0.5⎤ , and the total row number is LPCBC/LPGAF when the target field is large enough as
follows:
⎡2w /(3r ) + 1 / 3⎤ . So the number of clusters by CBC
13l 13w
algorithm which’s denoted by CNCBC can be obtained +
as follows: LPCBC 3R 3R 39l + 13 w
lim = lim = (7)
⎧⎛ ⎡
l →∞ , w→ ∞ LPGAF l →∞ , w →∞ 5l 5w 45l + 45 w
l ⎤ ⎡ l 1 ⎤ ⎞⎡ 2w 1 ⎤ +
⎪⎜ ⎢ ⎥+⎢ + ⎥ ⎟⎢ + ⎥/2 R R
⎪⎜ ⎢
⎝ 3r ⎥ ⎢ 3r 2 ⎥ ⎟ ⎢ 3r 3 ⎥
⎠
⎪ 25
⎪ ⎡ 2w 1 ⎤
⎪ when ⎢ + ⎥ is even CBC
⎪ ⎢ 3r 3 ⎥
CNCBC= ⎨ , 20 GAF
The average length
⎪⎛ ⎡ l ⎤ ⎡ l 1 ⎤ ⎞⎛ ⎡ 2 w 1 ⎤ ⎞ ⎡ l ⎤
⎪⎜ ⎢
⎜ ⎥+⎢ + ⎥ ⎟⎜ ⎢
⎜ 3r + 3 ⎥ − 1⎟ / 2 + ⎢
⎟ ⎥
⎪⎝ ⎢ 3 r ⎥ ⎢ 3 r 2 ⎥ ⎟⎝ ⎢
⎠ ⎥ ⎠ ⎢ 3r ⎥ 15
⎪
⎪ ⎡ 2w 1 ⎤
when ⎢ + ⎥ is odd 10
⎪
⎩ ⎢ 3r 3 ⎥
where r=R/ 13 (3) 5
We can compute the asymptotic value of
CNCBC/CNGAF when the target field is large enough as 0
follows: 5 6 7 8 9 10 11 12 13 14 15
13l ⎛ 2 13 w 1 ⎞ The width of the rectangle (102m)
⎜ + ⎟
CN CBC 3 R ⎜ 3R
⎝ 3⎟⎠ 676 Figure 5 The average length of inter-cluster
lim = lim = (4) communication path for different shape of
l → ∞ , w → ∞ CN
GAF
l →∞ , w →∞
5l 5w 675
rectangles
R R
From above we can see LPCBC<LPGAF. In the special
So the number of clusters generated by CBC
case of l=w, the ratio is about 0.734. Subsequently we
algorithm is approximately equal to GAF algorithm.
analyze the average length of inter-cluster
Next we analyze the length of inter-cluster
communication path of CBC algorithm and GAF
communication path of CBC algorithm and GAF
algorithm by simulation. The transmission range of
algorithm respectively. The shorter the length of inter-
node is set to be R=100m. The length of the target
cluster communication path, the more energy is saved.
rectangle is set to be l=1500m. The width of the target
The longest inter-cluster communication path of GAF
rectangle w is varied from 500m to 1500m. Figure 5
algorithm is the communication path between the grid
shows the average length of inter-cluster
at left down corner and the grid at right up corner. Let
communication path of CBC algorithm and GAF
LPGAF denote it length, which can be obtained as
algorithm for different shape of rectangles. It can be
follows:
seen that the average length of inter-cluster
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5. communication path of CBC algorithm is smaller than regular hexagon. Sensor nodes belonging to the same
GAF algorithm in all cases. When the target region is a cell form a cluster. The size of cells is selected to be
square, it’s about 78.6% of GAF algorithm. The ratio R/ 13 so that any node in adjacent cell can
of CBC algorithm to GAF algorithm is about 79.4% on communicate with each other, where R is the
average. transmission range of sensor node. We present an
140 algorithm of calculating which cell a sensor node
belongs to from its coordinate. We also present a low-
CBC
The network lifetime (day)
120 cost local algorithm for electing cluster head. And we
GAF
100 give a method of routing that can produce the optimal
inter-cluster communication path.
80 We evaluate the performance of our proposed CBC
60 algorithm with comparing to GAF algorithm. By
analysis, the numbers of clusters generated by CBC
40 algorithm and GAF algorithm are approximately equal,
20 but the largest length of inter-cluster communication
path of CBC algorithm can reach 73.4% of that of
0 GAF algorithm at most. Simulation results show that
4 5 6 7 8 9 10
the ratio of the average length of inter-cluster
The number of sensor nodes (103)
communication path of CBC algorithm to that of GAF
Figure 6 The network lifetime for different algorithm is 79.4% on average, and the network
number of sensor nodes lifetime by CBC algorithm can be prolonged by about
Finally we compare the network lifetime by CBC 10% with comparison to GAF algorithm.
algorithm with GAF algorithm by simulation. The
transmission range of node is set to be R=100m. The 6. Acknowledgement
target rectangle is set to 1000×1000m2. The number of This paper was supported by Guangdong Natural
sensor nodes is varied from 4000 to 10000. The battery Science Foundation (2008254), Science Foundation for
package of sensor nodes can supply 2200mAh at 3V, so Youths of Shenzhen University (200869), National
initial energy of each node is 23.76kJ. We use the radio Science Foundation of China (60602066), Foundation
model described in [13]: The radio spends 200nJ/bit to of Shenzhen City (JC200903120069A and
transmit 1-bit and spends 100nJ/bit to receive 1-bit SG200810220145A).
over a transmission range of 100m. Communications in
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