An Unequal Clustering Algorithm for Wireless Sensor Networks
E. Ever
, R. Luchmun
, L. Mostarda
, A. Navarra
and P. Shah
CCM Department, School of Engineering and Information Sciences, Middlesex University, London NW44BT, U.K.
Department of Mathematics and Computer Science, University of Perugia, 06123 Perugia, Italy
Clustering, Multi-hop, Power Management, Residual Energy.
Prolonging the lifetime of wireless sensor networks has always been a determining factor when designing and
deploying such networks. Clustering is one technique that can be used to extend the lifetime of sensor networks
by grouping sensors together. However, there exists the hot spot problem which causes an unbalanced energy
consumption in equally formed clusters. In this paper, we propose UHEED, an unequal clustering algorithm
which mitigates this problem and which leads to a more uniform residual energy in the network and improves
the network lifetime. Furthermore, from the simulation results presented, we were able to deduce the most
appropriate unequal cluster size to be used.
Wireless Sensor Networks (WSNs) are usually self-
forming, self-healing networks that interact with their
environment to monitor or sense physical parame-
ters such as temperature, acoustics, vibration and hu-
midity among others. They are usually composed of
fixed, spatially distributed sensors and a base station
(BS). The main functions of a sensor node in a WSN
are sensing the environment, processing the raw val-
ues and transmitting them to a nearby node until they
reach the base station. The role of the base station
is to collect all those data received over time, analyse
them and ultimately make decisions based on whether
certain thresholds have been exceeded or not.
WSNs can operate in two modes: continuous peri-
odic sensing and transmission or event-triggeredsens-
ing followed by transmission. To decide on which
mode of operation to use is highly application de-
pendant. WSN, being a relatively new technology,
leads to many challenges, some of which have still not
been met completely. These are the real time, power
management, security and privacy factors (Karl and
Willig, 2005). The energy challenge is considered
to be very important because in most typical us-
ages, WSN nodes are deployed with a limited, non-
renewable source of energy, on which the lifetime of
the network will depend. One of the solutions put for-
ward by researchers is clustering.
In the clustering operation of WSNs, nodes are pa-
rtitioned into a number of small groups called clus-
ters. Each cluster has a coordinator, known as a Clus-
ter Head (CH), and a number of member nodes which
communicate only to their CH in order to transmit
data. Clustering offers some advantages such as data
aggregation done at the CH level, distribution of load
across all nodes since the role of the CH is not per-
manently fixed to one particular node; hence rotation
of CH is present. CH handles two types of traffic:
intra-cluster and inter-cluster communication; the for-
mer being communication between member nodes of
a cluster and the CH and the latter being the transmis-
sion/relay of packets from CH to CH until it reaches
the BS. Inter-cluster communication can make use of
either single hop or multi-hop forwarding (Zhao and
Wang, 2010). In single hop forwarding, each CH di-
rectly transmits to the BS, which can cause excessive
use of energy for the CH furthest away from the BS
making them critical nodes. However, in multi-hop
clustering, nodes nearest to the BS tend to deplete
their energy the fastest since they are burdened with
heavy relay traffic from the rest of the network in ad-
dition to their own intra-cluster traffic share. Those
nodes closer to the BS tend to die earlier than the rest
and as a result, sensing coverage gets reduced and
network partitioning becomes apparent, (Zhao and
Wang, 2010; Li et al., 2005; Xuhui et al., 2009; Kim
et al., 2008) which is defined as the hot spot problem.
Nevertheless multi-hop data transmission from source
to BS is usually more energy efficient due to the na-
Ever E., Luchmun R., Mostarda L., Navarra A. and Shah P..
UHEED - An Unequal Clustering Algorithm for Wireless Sensor Networks.
DOI: 10.5220/0003804001850193
In Proceedings of the 1st International Conference on Sensor Networks (SENSORNETS-2012), pages 185-193
ISBN: 978-989-8565-01-3
2012 SCITEPRESS (Science and Technology Publications, Lda.)
Figure 1: Residual energy of cluster heads (r=20m).
ture of the wireless channel (Zhao and Wang, 2010).
In this paper, an unequal clustering algo-
rithm (UHEED), based on the HEED algorithm (You-
nis and Fahmy, 2004), is proposed. HEED is a hy-
brid energy efficient distributed algorithm which uses
2 parameters to form equal sized clusters: residual en-
ergy of a node and node degree or the node proximity
to its neighbours. HEED does not make any assump-
tions about network topology, size and distribution or
density of nodes. UHEED creates unequal sized clus-
ters based on the distance of the CH from the BS. The
further away a cluster head is from the BS, the larger
will be its competition radius and hence the cluster
size will be bigger compared to those clusters formed
nearer to the BS. By creating unequal sized clusters,
the amount of intra-cluster traffic is considerably re-
duced for the CH’s nearer to the BS.
We also attempt to find the right cluster size based
on distance from the BS. We first demonstrate that
the hot spot problem actually exists in equal size clus-
ters (HEED) and use this as a comparison basis with
UHEED. From the analysis of the simulation results;
UHEED effectively mitigates the hot spot problem
of equal sized clusters and thus balances the energy
levels of CHs in the network, provided appropriate
sized cluster have been formed. Our simulation re-
sults also indicate that the network life-time is signifi-
cantly improved when compared with HEED (Younis
and Fahmy, 2004), LEACH (Heinzelman et al., 2000)
and unequal LEACH (Ren et al., 2010) based cluster-
ing algorithms.
The rest of this paper is organised as follows: Sec-
tion 2 presents most recent research within the area of
clustering algorithms in WSNs; Section 3 describes
the HEED algorithm and how we changed it to de-
velop UHEED; Section 4 describes the UHEED al-
gorithm, the radio and the network models used, the
competition radius formula and the simulator built in
Java to test this algorithm. Section 5 presents the sim-
ulation study conducted for different test cases and
a comparison of the results with recent advances in
clustering in WSNs. Finally, the paper is concluded
along with an opportunity to extend the work further
in Section 6.
There have been a number of (equal and unequal)
clustering algorithms proposed for wireless sensor
networks in recent years. Existing studies on unequal
clustering approaches are considered in this section.
An unequal clustering model was first proposed
in (Soro and Heinzelman, 2005) based on unequal
clustering size (UCS) in order to balance the energy
level or energy consumption of cluster heads due to
heavy inter-cluster relay traffic. Their simulations
assumed that cluster heads were located at prede-
SENSORNETS 2012 - International Conference on Sensor Networks
Figure 2: Residual energy of cluster heads (r=50m).
termined locations and involved using heterogenous
node structure. In the case of multi-hop networks, it
was demonstrated that UCS was 10-30 % better than
existing equal clustering models.
In the energy efficient unequal clustering (EEUC)
algorithm (Li et al., 2005), the authors propose
another unequal clustering algorithm where nodes
join clusters of unequal size. However, according
to (Gong et al., 2008), EEUC may produce lone
nodes since the cluster head election is probabilis-
tic. Zhao et al. propose an unequal layered clus-
tering approach for large scale wireless sensor net-
work (ULCA) (Zhao and Wang, 2010) which assumes
a BS at the centre of the grid and creates layers. The
layers closer to the base station are smaller in size
giving the inner layers more residual energy for inter-
cluster traffic. When compared to EEUC (Li et al.,
2005), ULCA has a better network lifetime and the
overhead for clustering the network is much lower be-
cause of the inherent local join and local broadcast
In (Gong et al., 2008), a Multi-hop Routing
Protocol with Unequal Clustering (MRPUC) is pro-
posed which bears similar characteristics of the al-
gorithm mentioned in (Karl and Willig, 2005; Li
et al., 2005). A comparison study conducted in (Gong
et al., 2008) demonstrates that MRPUC outperforms
an equal clustered version of itself by extending the
network lifetime by 34.4%.
In (Heinzelman et al., 2000), the Lower Energy
Adaptive Clustering Hierarchy (LEACH) protocol is
presented. The algorithm elects cluster heads solely
based on probability. No residual energy is taken into
account. Moreover, cluster heads use the single hop
communication model to forward packets to the base
station. A refined version of LEACH can be found
in (Xuhui et al., 2009). The lifetime of the sensor net-
works is maximised by first forming unequal clusters,
and then a new threshold algorithm, based on residual
energy, is used to elect cluster heads.
In (Yu et al., 2011), an energy-driven unequal
clustering (EDUC) algorithm is proposed which dis-
cusses the rotation of the role of CH based on either
time-driven CH rotation or energy-drivenCH rotation
approach. In EDUC, it is discussed that the energy-
driven CH rotation is better since a new CH is elected
only when the energy of the current CH has fallen be-
low some set threshold value and since the election is
local, this avoids global topology reconstruction and
downtime. In EDUC unequal clusters are formed by
having unequal competition ranges and each node can
be a cluster head only once during the sensor net-
work lifetime. One drawback of EDUC is that it
uses single-hop inter-cluster transmission and accord-
ing to (Zhao and Wang, 2010), multi-hop is better.
A totally new approach is proposed in (Jaichan-
dran et al., 2010) to mitigate the hot spot problem in
WSNs in which an area S is divided into N number of
UHEED - An Unequal Clustering Algorithm for Wireless Sensor Networks
Figure 3: Network lifetime for 500x500 grid with 1000 nodes.
cells, each having at least 1 sensor node and the sen-
sor nodes cooperate with neighbour nodes to forward
sensed data to the base station. Sensor nodes near the
base station act as gateway nodes (G nodes) which
tend to die earlier as they have to relay heavy traffic.
The novel approach in (Jaichandran et al., 2010) is to
introduce additional sensor nodes in the gateway area
to help in the relay of traffic to the base station. Al-
though, results indicate that adding an arbitrary num-
ber of G nodes does not improve performance, instead
a calculation of optimal number of G nodes is first re-
quired which, then needs to be added to improve and
extend the lifetime of the network.
Recent research in (Bagci and Yazici, 2010) pro-
poses an energy aware fuzzy unequal clustering al-
gorithm (EAUCF) which uses 2 parameters in or-
der to calculate the competition range of the clus-
ter head. From the results obtained, EAUCF out-
performs EEUC (Li et al., 2005), ULCA (Zhao and
Wang, 2010) and LEACH (Xuhui et al., 2009) for all
the performance measures.
In (Pin et al., 2010), the authors propose IEEUC,
which is similar to the study in EEUC (Li et al., 2005),
since it creates unequal sized clusters as they are fur-
ther away from the base station, to mitigate the hot
spot problem. The main difference between IEEUC
and EEUC lies in the competition radius calculation.
IEEUC uses the node degree factor, which is based
on the number of hops to the base station, to calcu-
late the competition radius. In EEUC, even clusters
equidistant from the BS may have different number
of member nodes, either too many or too few. On the
other hand in IEEUC, we do not have this problem.
The authors of (Nam et al., 2010) propose a vari-
ant of the LEACH algorithm by including the residual
energy parameter in the calculation of the threshold T.
In the original LEACH algorithm, a node generates a
random valueU [0, 1] and if that value is less than T,
it becomes a cluster head and also, if p is the ratio of
cluster heads, a node can be a cluster head only once
during the 1/p round. In (Nam et al., 2010) a new
threshold formula is used to allow a cluster head to
be re-elected based on residual energy and it is shown
that this new threshold increases the network lifetime.
In (Ren et al., 2010), yet another version of LEACH is
presented. Two parameters are used in the setup phase
of electing cluster heads: energy ratio (current energy
to initial energy) and competition radius. Similar to
the study in (Nam et al., 2010), this technique allows
cluster heads with more residual energy to be elected.
In addition, (Ren et al., 2010) attempts to solve the
hot spot problem by creating unequal sized clusters
by varying the competition radius. Smaller clusters
will be formed near the base station while larger ones
will be created as they are further away from it.
In this paper, we introduce an unequal variant of
HEED (UHEED). While HEED defines an equal clus-
ter size, UHEED makes use of a competition radius
formula which creates unequal clusters. We com-
pare UHEED with the HEED, LEACH and unequal
LEACH algorithms described in (Younis and Fahmy,
2004), (Heinzelman et al., 2000), and (Ren et al.,
2010), respectively.
SENSORNETS 2012 - International Conference on Sensor Networks
Figure 4: Network lifetime for 100x100 grid with 300 nodes.
Hybrid Energy Efficient Distributed (HEED) is a dis-
tributed clustering algorithm in which two parameters
are used to determine the eligibility of a node to be-
come a cluster head. Since prolonging the network
lifetime is the main goal, residual energy is used as the
first parameter, which allows those nodes with higher
residual energy to become cluster heads, thus balanc-
ing the overall energy of the network. The second
factor intra communication cost, which can be clus-
ter density, allows a node to join a CH with the least
number of nodes so as to reduce the load of the intra-
cluster traffic on the CH. HEED does not make any
assumption about the network such as density or size.
The HEED algorithm is run by each node and is
in 3 stages:
In the Initialisation stage, an initial percentage of
CH among N nodes is set (C
) which has no impact
on the final number of CH to be formed at the end of
the algorithm and as such is only necessary to limit
the initial number of broadcast. Each node calcu-
lates its probability (CH
) of becoming a CH. The
is not allowed to fall below a certain threshold
in order for the algorithm to terminate in O(1)
In the Repeat stage, those nodes that could not join
a CH, elect to become a tentative CH and send an an-
nouncement. This phase iterates itself and each time
the CH
value doubles until it becomes 1. During
the iterations, the node can also decide to find a CH
instead of becoming one itself.
In the Finalise stage, a node decides its status to
become a final CH for the current round or joins the
least cost cluster.
Once the clustering process is over, the network
enters a data transfer phase. Clustering will occur
again after some time in order to rotate the role of the
CH and thus balance the energy levels in the network.
In this phase, each node of a cluster forwards data to
the CH which in turn forwards the aggregated data of
its members in a multi-hop fashion (CH to CH) until
the base station (BS) is reached.
The problem here is that those nodes nearer to the
BS deplete their energy faster than those located fur-
ther away. This excessive inter-cluster traffic near the
BS causes the nearby nodes to die earlier reducing the
overall network lifetime.
In UHEED, we attempt to solve the problem of
nodes nearer to the BS dying earlier. In HEED, each
CH uses the same competition radius, irrespective of
its distance from the BS, hence on average having the
same number of nodes. UHEED uses the competition
radius formula from EEUC (Li et al., 2005), which
UHEED - An Unequal Clustering Algorithm for Wireless Sensor Networks
creates smaller clusters as the BS is neared.
This overall can improve the network lifetime for
multi-hop WSNs which will be shown using simula-
tions. This allows less intra-cluster traffic for the CHs
near the BS and hence more energy is allocated to the
inevitable higher load of relay traffic.
In this section, the proposed algorithm is described in
detail. Although uneven clustering methods have ex-
tensively been discussed in the related works, the un-
even clustering approach have not been used together
with the well known HEED algorithm. It is necessary
to analyse the system parameters in order to provide
right cluster sizes for the HEED algorithm with un-
even cluster sizes (UHEED).
4.1 Network Model
The network model introduced uses a two dimen-
sional representation of the environment and the
nodes are deployed randomly following a uniform
distribution. We make the following assumptions
about nodes: (i) all nodes are homogeneous in terms
of energy, communication and processing capabili-
ties;(ii) each node is identified with a unique ID; (iii)
nodes can transmit at various power levels depending
on the distance of the receivers; (iv) nodes are not mo-
bile that is they remain stationary after the uniformly
distributed deployment process; (v) communicating
nodes can establish the distance among them
; (vi)
all nodes know their distance from the base station.
The BS is located away from the sensing grid with
no energy concerns at all, and it is considered to be a
node with enhanced communication and computation
capabilities. The BS is not mobile. The data captured
in a cluster is highly correlated, therefore it can be ag-
gregated before being transmitted to the base station.
A network operation model similar to that of
(Younis and Fahmy, 2004) consisting of multiple
rounds is used. A round starts by triggering the
clustering mechanism and after clusters have been
formed, the network goes into a data exchange
phase. This includes intra-cluster communication
where each sensor node sends exactly one message
to its cluster head and inter-cluster communication
where each aggregated data is sent by the cluster head
to the BS (multi-hop data transmission among cluster
Usually nodes estimate the approximate distance by the
strength of the signal received, since the transmission power
level is known (unless there is multi-path fading problem).
heads is performed). The round ends when all aggre-
gated data sent by the cluster heads are received at the
base station.
The radio model employed uses both the free
space and the multi-path channel model and assumes
error-free communication links.The simulation pa-
rameters used are similar to those in (Younis and
Fahmy, 2004). A sensor spends E
= 50nJ/bit
(Younis and Fahmy, 2004) to run the transmitter or
receiver circuitry. The energy spent by the transmitter
amplifier E
will depend on the distance d between
the sender and the receiver: E
= E
assuming a free
space model when d < d
and E
= E
a multipath model when d d
, where d
= 75m is
a constant distance. E
= 10pJ/bit/m
and E
. In order to transmit a k-size packet
over a distance of d using the above radio model, the
amount of energy consumed for transmission E
, can
be calculated as:
= (E
× k) + (E
× k × d
), (1)
where, n = 2 for the free space model and n = 4 for
the multipath model. The amount of energy E
to receive a k-bit size message is:
= (E
× k) (2)
4.2 Simulation Model
UHEED is based on the HEED algorithm (Younis
and Fahmy, 2004), however, unlike HEED it uses the
competition radius formula given below, in order to
create unequal clusters. Since the lifetime of the lead-
ers closer to the BS is more critical, the clusters fur-
ther away have larger sizes compared to the clusters
close to the BS.
1 c
is the maximum competition radius which
is predefined. In this work it is defined as the diagonal
distance of the sensing grid area divided by 10.
and d
are the maximum and minimum dis-
tance between sensor nodes and the base station; c is
a constant coefficient between 0 and 1.
For the simulation we perform various consecu-
tive rounds (explained in Section 4.1). These are per-
formed until the network is dead. The network is
considered dead when all nodes have depleted 99.9%
of their energy. Network lifetime is based on rounds
rather than clock time, and the simulation model used
is event triggered. In other words, the simulation
clock is always set to the time of the next event un-
til the network dies.
SENSORNETS 2012 - International Conference on Sensor Networks
Figure 5: Network lifetime for 200x200 grid with 400 nodes.
Figure 6: Residual energy comparison unequal leach vs UHEED.
In this study, a simulation program is employed in or-
der to evaluate the proposed UHEED algorithm. The
simulation program is first validated by using the nu-
merical results presented in the existing literature
(Younis and Fahmy, 2004). For the validation, a grid
with dimensions 2000 × 2000 metres is considered
and 1000 nodes are deployed. The cluster radius is
taken from 20m to 400m and each experiment value
is obtained for an average of 100 runs. The numerical
results shows that our implementation of the HEED
UHEED - An Unequal Clustering Algorithm for Wireless Sensor Networks
algorithm exhibit similar behaviour as in(Younis and
Fahmy, 2004).
5.1 Existence of Hot Spot Problem in
Equal Size Clusters
The results presented in this section are related to the
HEED equal clustering algorithm. More specifically,
the HEED algorithm has been run for one round, and
figures 1 and 2 clearly show that cluster heads nearer
to the base station have lower residual energy com-
pared to that of cluster heads further away. The results
presented are for cluster radiuses of 20m and 50m,
however the behaviour is the same for different clus-
ter sizes as well.
5.2 Network Lifetime
In this section the lifetime of UHEED is evaluated by
running simulations with different parameters of grid
size and number of nodes.
When comparing UHEED and HEED the same
parameters from (Younis and Fahmy, 2004) have been
used. The base station is located at lower right side of
the grid, E
= 50nJ/bit, E
, num-
ber of nodes 300 to1000 and the initial Energy = 2J.
More specifically, we have used two settings: (A) a
grid size of 500m x 500m with 1000 nodes; (B) a grid
size of 100m x 100m with 300 nodes. We have en-
sured there is the same number of cluster heads in
both UHEED and HEED. This ensures that the two
algorithms perform the same number of hops in the
inter-cluster communication. Figures 3 and 4 show
the best and worst case scenario, for network life time,
for UHEED and HEED for:
Case(A): The results show that UHEED outper-
forms HEED in the best scenario with c = 0.8 for
UHEED and r = 35m for HEED; but for the worst
case, UHEED and HEED both follow a similar pat-
tern with the last node dying after around 500 rounds.
In the best case scenario, the last node for UHEED
dies after round 3325 and for HEED, it dies after 900
rounds which is evident in Figure 3. Overall, there is
a 250% increase in network lifetime for UHEED in
the best case scenario.
Case(B): UHEED outperforms HEED in both the
worst and best scenarios. In the best case scenario, the
last node in UHEED dies after 4750 rounds, where
as, in HEED, it dies after 3340 rounds, which can be
observed in Figure 4. Overall, there is an increase of
more than 40% network lifetime for UHEED in the
best case scenario.
When comparing UHEED, LEACH and unequal
LEACH the same parameters from (Heinzelman et al.,
2000) and (Ren et al., 2010) have been used. More
specifically, the base station is outside the grid, E
= 50nJ/bit, E
, number of nodes 400
and the initial Energy = 0.3J.
UHEED is compared to Unequal LEACH (Ren
et al., 2010) and results are shown in Figure 5. The
best and worst case for UHEED and Unequal LEACH
are considered. For Unequal LEACH we have used
the parameters found in (Ren et al., 2010) with a grid
size of 200 by 200 and 400 nodes. In order to com-
pare UHEED to Unequal LEACH, the data exchange
phase of UHEED has been modified to a single-hop
data transmission since Unequal LEACH is a single-
hop protocol.
In the simulation study between UHEED and Un-
equal LEACH, it can be observed from Figure 5 that
UHEED outperforms Unequal LEACH by a factor of
more than 100% when network lifetime is considered.
Figure 6 shows the residual energy for UHEED,
Unequal LEACH and LEACH with respect to First
Node Dead (FND) and Half Node Alive (HNA). The
residual energy is obtained by calculating the residual
energy of the entire network. As can be seen from
the Figure 6, in UHEED after the first node is dead,
the overall residual energy level for all the cases from
c = 0.1 to c = 0.9 is much higher than LEACH or Un-
equal LEACH. Also, it is observed that when half of
the nodes are alive, the residual energy level in case
of UHEED is comparatively higher than LEACH and
Unequal LEACH. Hence, from the results seen in Fig-
ure 6 for residual energy levels and Figure 5 for the
network lifetime, it is seen that the lifetime degrada-
tion of UHEED is graceful. This means that not many
nodes die very quickly and then the network has very
few nodes which are alive for a longer duration, but,
as observed in Figure 6, after half the number of nodes
are dead in the case of UHEED, there is still higher
residual energy level availablefor the rest of the nodes
to continue operation with respect to LEACH and un-
equal LEACH.
It is worth mentioning that, for UHEED we have
used HEED together with the algorithm employed for
EEUC to compute the size of the clusters. More
specifically, the HEED clustering method has been
improved by implementing it together with the com-
petition radius formula of EEUC. The simulation re-
sults clearly show that this combination performs bet-
ter than HEED, LEACH and unequal LEACH. How-
ever, the EEUC algorithm was not considered for
comparison. In fact, in (Li et al., 2005), the numerical
results presented for the number of alive sensors show
that EEUC has very little improvement compared to
the HEED algorithm. Furthermore, when the energy
consumptionsare compared, results of two algorithms
SENSORNETS 2012 - International Conference on Sensor Networks
cross each other and they are better than one another
for various time intervals.
In this paper, we proposed an unequal cluster-
ing algorithm for wireless sensor network based on
HEED (Younis and Fahmy, 2004). A common prob-
lem in equal based cluster in sensor networks is the
hot spot problem. Our approach to provide a solution
was first to implement the HEED algorithm, show
that the hot spot problem really exists, and finally at-
tempt to mitigate it by creating UHEED. This algo-
rithm uses a competition radius formula which cre-
ates unequal clusters as they are further away from
the base station. This effectively allows more inter-
cluster or relay traffic and less intra-cluster commu-
nication for nodes nearer to the base station, hence
preventing their early death. Simulation performed
on the UHEED algorithm demonstrated that the life-
time of the network was increased in all test scenarios
compared to HEED, LEACH and Unequal LEACH.
An interesting study also conducted was regarding
the value of the constant c in the competition radius
formula. Simulation results showed that a value of
c = 0.8 achieved up to almost 250% improvement in
the network lifetime when compared to HEED and
almost 100% improvement when compared to un-
equal LEACH. During the course of this investiga-
tion, we found out that values like first node dead
(FND), half node alive (HNA) and last node dead
(LND) are somewhat affected by the density of the
network. Hence, our future work will be to investigate
the relationship between the network density and the
aforementioned parameters. A mathematical model
will also be developed in order to support the simula-
tion results presented in this paper.
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UHEED - An Unequal Clustering Algorithm for Wireless Sensor Networks