Wireless Sensor Network, 2009, 1, 316-323
doi:10.4236/wsn.2009.14039 Published Online November 2009 (http://www.scirp.org/journal/wsn).
AEESPAN: Automata Based Energy Efficient Spanning Tree for
Data Aggregation in Wireless Sensor Networks
Zahra ESKANDARI, Mohammad Hossien YA GHMAEE
Department of Computer Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Received May 6, 2009; revised July 5, 2009; accepted July 10, 2009
Abstract
In Wireless Sensor Networks (WSNs), sensor nodes are developed densely. They have limit processing ca-
pability and low power resources. Thus, energy is one of most important constraints in these networks. In
some applications of sensor networks, sensor nodes sense data from the environment periodically and trans-
mit these data to sink node. In order to decrease energy consumption and so, increase network’s lifetime,
volume of transmitted data should be decreased. A solution, which is suggested, is aggregation. In aggrega-
tion mechanisms, the nodes aggregate received data and send aggregated result instead of raw data to sink, so,
the volume of the transmitted data is decreased. Aggregation algorithms should construct aggregation tree
and transmit data to sink based on this tree. In this paper, we propose an automaton based algorithm to con-
struct aggregation tree by using energy and distance parameters. Automaton is a decision-making machine
that is able-to-learn. Since network’s topology is dynamic, algorithm should construct aggregation tree peri-
odically. In order to aware nodes of topology and so, select optimal path, routing packets must be flooded in
entire network that led to high energy consumption. By using automaton machine which is in interaction
with environment, we solve this problem based on automat learning. By using this strategy, aggregation tree
is reconstructed locally, that result in decreasing energy consumption. Simulation results show that the pro-
posed algorithm has better performance in terms of energy efficiency which increase the network lifetime
and support better coverage.
Keywords: Automata Learning, Wireless Sensor Networks, Data Aggregation, Energy Efficient, Spanning Tree
1. Introduction
Wireless Sensor Networks (WSNs) are networks that
consist of low power nodes with limited processing abil-
ity. These nodes have sensors which sense light, tem-
perature, jitter and etc. in the environment. These nodes
are deployed in environment densely and randomly. In
monitoring application, these sensor nodes sense data
from the environment periodically and transmit these
data to sink node. Since transmitting the data is the most
costly function in the network and power of the nodes is
limited and cannot usually be charged; this leads to de-
crease node’s power quickly.
After some rounds, network nodes energy is ran out
and this leads to situations which the network can not
work anymore. To the points mentioned above in order
to increase network’s lifetime, number of transmitted
data packet should be minimized [1,2].
Network nodes, after event occurrence and sensing
data from the environment, forward the sensed data to
the sink. In addition to sensed data, each node must
transmit other node’s data to the sink. As mentioned
above, data transmission consumes node’s energy
quickly. The solution which is suggested to decrease the
number of data transmissions is aggregation mechanism.
Aggregation mechanism works as follow: each node
senses data from the environment and receives other
node’s data, then aggregates these data, based on the
aggregation function and transmits the aggregation result
to the sink. Therefore aggregation decreases the data
volume that is transmitted and this leads to less energy
consumption. In addition to mentioned improvements,
aggregation decreases collision and retransmission delay
[3]. In aggregation algorithms, we must construct aggre-
gation spanning tree [4]. The spanning tree is a tree con-
tains all network nodes and doesn’t have any loop.
Like routing algorithms [5], aggregation algorithms
should also be aware of the network topology and based
on these information and queries which are propagated
by root, network nodes select aggregation function and

Z. ESKANDARI ET AL. 317
aggregate the data, and then forward aggregated data to
sink.
Cluster based algorithms [6] needs only local informa-
tion to construct aggregation tree, therefore they transmit
fewer packets to construct the aggregation tree.
In [7], authors investigate the computational complex-
ity of optimal data aggregation in sensor networks and
show that it is generally NP-hard; they present some
suboptimal data aggregation tree generation heuristics,
Center at Nearest Source (CNS), Shortest Paths Tree
(SPT) and Greedy Incremental Tree (GIT) and showed
the existence of polynomial special cases. Different ag-
gregation algorithms have been presented in recent years
[1,4,6,8–10].
Espan [4] is an energy-aware spanning tree algorithm
that constructs the aggregation tree to aggregate the data.
In Espan, the source node which has the highest residual
energy is chosen as the root and other nodes choose their
corresponding parent node among their neighbors based
on distance to the root and residual energy. In LPT [8]
after selecting the node with most energy as root, each
node selects neighbors with most energy as parent and its
parent forwards its data to the sink.
In this paper, we present an automata based Energy
Efficient Spanning tree (AEEspan) algorithm which is a
new energy efficient aggregation algorithm for wireless
sensor networks. The current work is a modified version
of our already published papers [1,11]. In [1] we propose
an energy aware data aggregation spanning tree algo-
rithm. In [11], we present an automata based algorithm to
construct spanning tree. Automata is an able-to-learn
decision-making structure that selects the best action
among a number of actions then wait for environment’s
response to this selection. By using the environment
feedbacks, automata update the probability of the selec-
tion of each action among the set of actions and select
best action for the next step. The main idea of proposed
protocol is as follow: each node has an automaton to
select the best nodes among its neighbors as its parent.
Since the status of the network is dynamic, the aggre-
gation algorithm should construct the routing tree peri-
odically. When a timer is expired our some nodes are
failed in the network, the new aggregation tree must be
constructed [4,8].
At the beginning of each time interval, routing packets
are flooded into the network. In each routing packet has
some routing information likes: number of hops to the
root, remaining energy, number of child node. Each node
selects optimal path to the sink, based on algorithm pa-
rameters. Since the node’s energy is limited, transmitting
and receiving this volume of routing information is not a
good solution to construct aggregation tree. This over-
head causes a lot of energy consumption. So, some nodes
run out of energy quickly and fail. This causes network
to be disconnected.
To solve this problem we use an automaton based ap-
proach; if a node in the aggregation tree fails, and a part
of tree is disconnected, only this part of tree starts to re-
construct. So it is not necessary to flood routing packets
into entire network. To do this, each node uses the envi-
ronment feedbacks, and updates its automata.
The remainder of this paper is as follow: in section 2,
we review some existing aggregation algorithms. The
system model is given in section 3. In section 4, we pre-
sent the proposed algorithm and the performance evalua-
tion of proposed algorithm is presented in section 5. Fi-
nally, section 6 concludes the paper.
2. Related Work
Different aggregation algorithms have been presented in
recent years. In this section we review them briefly. As
presented in [9], DCTC algorithm dynamically con-
structs the aggregation tree for mobile target tracking. In
the presented algorithm depending on the target location,
a subset of nodes participates in tree construction.
In [12], the sink saves the entire network state and
then by considering link cost, in centralized form, con-
structs the tree by minimum cost. In cluster algorithm [6],
after partitioning the network into clusters, cluster’s
members construct aggregation tree and transmit data to
cluster head. After aggregation, cluster heads transmit
aggregated data to the sink in one hop or multihop man-
ner [13].
Espan [4] is an energy-aware spanning tree algorithm
that constructs the aggregation tree to aggregate the data.
In Espan, the source node which has the highest residual
energy is chosen as the root and other nodes choose their
corresponding parent node among their neighbors based
on distance to the root and residual energy. One of the
most important problems of Espan is that the nodes with
least distance to root may be selected as parent by many
nodes. So these nodes consume their energy quickly and
then they will be failed sooner than other network nodes.
In LPT [8] after selecting the node with most energy
as root, each node selects neighbors with most energy as
parent forwards its data to the sink. In the mentioned
algorithm, when a node in the tree fails, the tree will be
reconstructed.
In [1] an energy efficient algorithm, which constructs
the aggregation tree, is presented. To prevent failing the
nodes and to increase the network lifetime, the algorithm
considers both the remaining energy and the distance
parameters. Each node selects a node which has the most
energy within neighbors as its parent. Furthermore, the
distance from this parent to the root must be reasonable.
To balance the energy and distance parameters, the algo-
rithm uses path’s energy and length parameters.
In [14], the proposed algorithm uses machine learning
to transmit the sensed data to the sink. Learning algo-

318 Z. ESKANDARI ET AL.
rithm is executed in the sink and its result is propagated
throughout the network. In [15] Q-leaner is used to con-
struct aggregation tree, to maximize aggregation ratio.
In [16] an algorithm to construct aggregation tree,
based on automata, is proposed. In this algorithm, in
which each node is equipped with an automaton, the
automaton selects a path for transmitting data via the
path which the aggregation ratio is maximized. In [17],
the algorithm considers an automaton for each node,
which selects a path to transmit data to the sink in ac-
cordance with network conditions.
3. System Model
We consider a network of N sensor nodes uniformly dis-
tributed over a region and one sink. These nodes are non
mobile. The sensor nodes have radio communications;
two nodes can receive and transmit data if they are in
communication range of each other. There are three
types of data collection in sensor networks [18].
Event-based data, such as intrusion detection or object
tracking, is collected when an event within the deploy-
ment region occurs. The event is confirmed by sensors
and reported to the sink. State-based data is collected in
response to a query sent to selected sensors requesting
relevant data. Global state-based data, such as tempera-
ture or humidity, is collected by sensors all over the de-
ployment area and is transmitted toward the sink. Our
interest here is in global state-based data. All sensor
nodes are sources, sense environment and transmit
sensed data to the sink periodically. In the following
subsections we describe the energy model and data
transmission model used in this work.
3.1. Energy Model
We use the same energy consumption model described in
[19]. In this model a sensor node consumes Eelec (J/bit)
in transmitter or receiver circuitry and Eamp (J/bit/m2)
in transmitter amplifier to achieve an acceptable signal
noise ratio. A sensor node expends energy ETij (k) or
ERi(k) in transmitting or receiving a k-bit packet to or
from distance distij, given by the following equations:

ijampelecij distkEkEkET ***)(  (1)
kEkER eleci *)(  (2)
The exponent λ heavily depends on the communica-
tion medium [20]. In the current work, we assume that
the transmission power is directly related to the squared
distance, means λ=2, which hold for free space. When
the distance is small, the free space propagation model is
adopted for energy loss, and when the distance is large,
the two-ray ground model is adopted for energy loss,
which means λ=4.
In the above functions, k represents the length of
transmitted and received data packet. Sensor nodes
transmit or receive two types of packet; routing packet
and data packet. Routing packets flood in the network to
construct or reconfigure the aggregation tree. Data pack-
ets include data which sense by nodes from environment
and are transmitted to sink. We assume the aggregation
function is simple, for example, max or average function,
so the input data length is equal to the output data length.
Based on this assumption, all data packets in the network
have the same length. According above descriptions, we
should try to minimize not only distance but also the
volume of transmitted and received packets.
As described in [6] if aggregation function is simple,
the energy consumption for data aggregation will be neg-
ligible.
3.2. Data Transmission Model
After determining children of a node, a node creates a
TDMA schedule and notifies its children about it. In the
data transmission phase, children send their data to their
parent according to the specified TDMA schedule. By
using TDMA scheduling mechanism, we can solve the
collision problem of data transmission, too. In addition,
after sending data each node goes to sleep mode until
next round, which cause power saving.
As described in [20], round is defined as the collection
of one data unit from every node in the network and de-
livering the resulting aggregated data to the sink node. In
every round, each parent in the tree will wait till it re-
ceives data from all its children. A node after participat-
ing in a round, wait until next round. Based on [20], life-
time of a tree is defined as the number of rounds that can
be performed before the failure of certain percentage of
total nodes. Therefore, in this paper, lifetime is defined
as the failure of 10% of the total nodes of the tree.
3.3. Automata
Learning automata is an abstract model which has a fi-
nite set of actions as its input. Each member of the input
set has a selection probability parameter. Automata se-
lect an input with highest selection probability as their
output. Then the environment evaluates the selected ac-
tion and responses to the automata. Automata use the
response for learning process.
Learning process is as follow: if the environment re-
sponse is unfavorable based on network parameter, the
automata penalize the selected input by decreasing its se-
lection probability and increasing selection probability of
the other members of the input set members. But if the
environment response is favorable, the automata reward the
selected input by increasing its selection probability and
decreasing selection probability of the other members of

Z. ESKANDARI ET AL. 319
the input set. The rewarding process increases selection
probability of the awarded input for the next step.
As seen in Figure 1, an automaton is learned based on
the feedback of the environment.
As described above, an automaton is defined by the
quadruple {α, β, P, T} in which α= {α1, α2, α3… αn} rep-
resent the output set, β= {β1, β2, β3… βm} represent the
input set, P= {p1, p2, p3… p4} represent probability set
and finally p (i+1) = T [α, β, P] represent the learning
process.
4. Proposed Algorithm
As mentioned in section 1, data aggregation tree con-
struction algorithms construct tree periodically. To con-
struct an aggregation tree, at the beginning each period,
routing packets are flooded into the entire network to in-
form all nodes. After this step, each node selects the best
path toward the sink node and transmits data via selected
path until the next period. Transmitting these routing
packets periodically consumes a lot of energy and has
unfavorable overhead for the network.
In automata based algorithms [17,16], at the beginning,
routing packets are flooded into the entire network. Each
node considers each neighbor as entry in its routing table
and then calculates the selection probability of each entry
based on the algorithm’s parameters, energy or distance
and etc., and then each node selects the neighbor with
highest selection probability as its parent and sends its
data via this parent to root.
In [16] after receiving data, root sends acknowledg-
ment to the sender node; this acknowledgment has some
information for automata. Based on acknowledgment
information, automata penalize or reward the path’s
nodes, on the way that if the selected path was optimal
based on network parameters, selection probability is
increased for the next step, but if selected path was not
optimal, selection probability is decreased for next step.
This process is called automata learning.
In the next steps, each node selects a new parent based
on the updated selection probability of the nodes in the
network and this process is repeated by the end of the
network’s lifetime. By using of this property of automata
-learning-the algorithm prevents flooding the routing
packets periodically, at the same time, by using ack in-
formation, nodes are aware from changes in network to-
pology and paths are updated.
Figure 1. Learning automata.
Proposed algorithm works as follow: at the beginning,
routing packets are flooded into the network by the way
that each node sends its energy and the distance to root to
all its neighbors. Each neighbor, after receiving this mes-
sage, considers the sender as a new entry in its routing
table, and puts sender ID, sender energy and sender dis-
tance to root as entry fields.
This sends/receives is performed in entire network, so
each node maintains neighbors information in its routing
table. Then the routing table entries are considered as
input set of automata and the automata calculate the se-
lection probability of each entry as follow:
j
j
icedis
energy
CprobSel tan * (3)
In Equation (3), Ci is a constant which is calculated by
node and is depended on the sum of energy and distance
to root of entries in routing tables of node i. This means
that node i adds energy and as well distance to root of all
the input set members. Then automaton considers the
result of dividing the entry energy by its distance to root
multiply a fixed number (Ci) as the selection probability
of the entry.
Each node selects neighbor with highest selection prob-
ability as its parent, nodes in the network sense data and
aggregate them with collected data from their child, then
send the result of aggregation to their parents. Their par-
ents forward data to the sink by repeating this process.
In fact, trees show paths that each algorithm selects for
transmitting data to sink. These paths have an important
effect on energy consumption, if the algorithm selects
shortest paths mostly, the nodes in these paths fail quickly,
and in continue nodes must send their data via other paths
that my be longer, which led to high energy consumption,
decrease lifetime and disturb coverage of the network.
And as well, if the algorithm selects paths by considering
energy parameter as main parameter and does not regard
to path’s length, nodes send data via longer paths which
causes to high energy consumption. Thus, the algorithms
should consider parameters, not one parameter, and bal-
ance between these parameters.
In these work, we try to select an optimal path by con-
sidering both parameters-energy and distance-as main
parameters and construct the tree based on both of them.
In order to update automata, each node must collect
some information from the network. By using this infor-
mation, an automaton becomes aware of network chang-
ing. In [17] to be aware of the network state, each node
after receiving data sends feedback or acknowledgment
message to the sender of the data and as mentioned before,
this message has some information. By using these feed-
backs, automata penalize or reward the selected parent,
but sending these acknowledgments have a lot of over-
head. In [16] to decrease this overhead, acknowledgment
is sent after some data transmissions.

320 Z. ESKANDARI ET AL.
In the proposed algorithm, to be aware of network’s
changes, one solution that was presented in [11] worked
as follow: each node broadcasts its energy and distance to
root, in data packet, and does not send in a separate
packet, so, node’s neighbors, after receiving these packets,
update their routing tables. This procedure, perform
automata learning. Since node’s information of network
is updated, optimal path to root is continuously selected.
But, transmitting these addition data led to waste en-
ergy because parent’s energy becomes less than other
nodes in neighborhood after some rounds, mostly. Thus,
transmitting additional data in each data packet, based on
energy model that mentioned in section 3. A wastes en-
ergy.
So, we can improve algorithm performance by working
as follow: If a node fails in aggregation tree or the node’s
energy is lower than a pre determined threshold, then the
node’s children select a new parent from the nodes in
their neighborhoods. Then, it is not necessary to recon-
struct aggregation tree globally and periodically. By using
this strategy the tree is reconstructed when it is needed,
and reconstruction packet broadcast locally. This leads to
reduction in data transmission in the network and power
saving.
Thus, the reconstruction section of proposed algorithm
works as follow: by failing a node in tree, node’s children
select a new parent base on their automata inputs; each
node’s children broadcasts an update packet. The
neighbors, after receiving this packet, send their informa-
tion to packet’s sender. Then, each sender node updates
its automata and then, an input with highest selection
probability is selected as a new parent. By using this
property, we prevent flooding the routing packets, and
also, nodes are aware from changes in the network topol-
ogy and paths are updated. This process is repeated by the
end of the network’s lifetime.
In this work, the input and output sets-α, β- of each
node’s automaton are the entries of its routing table, and
the probability set-P-is the set of selection probability of
entries. To increase efficiency in proposed algorithm,
learning process does not perform each round, but when
energy consumption reaches a threshold, automaton,
based on responses from environment, performs learning
process.
Reconstruction property is an important section in tree
construction algorithm that is noted rarely. In this work,
we try to achieve two main goals:
·Construct an energy efficient tree by considering both
energy and distance parameters.
·Add the reconstruction property, to prevent from
flooding packets globally.
The pseudo code of the proposed algorithm which
helps us to understand the details of the proposed algo-
rithm is given in Figure 2. In this pseudo code, m repre-
sents the message which is sent by each node and con-
tains three fields: node's ID, node's energy and node's
distance to root. Input of AEEspan algorithm is the net-
work nodes vector.
5. Performance Evaluation
In this section, using computer simulation, we evaluate
the performance of the proposed algorithm and compare
it with other algorithms [1,4,8] algorithm. We call the
algorithm presented in [1], EEspan in below figures.
We consider a sensor networks with N sensor nodes
randomly arranged in a 600m×600m region. The number
of nodes (N) varies from 300 to 700. The initial energy
of each node varies from 8J to 20J. The communication
range of all nodes is set to 60 meter. The size of sensor
data packet is 320 bits and a routing packet is 30 bits
length. In the following curves the average values over
20 simulation experiments are depicted. Also, we assume
all nodes in the network sense the area periodically and
send their data to the sink node.
Figure 2. The pseudo code of the proposed algorithm.

Z. ESKANDARI ET AL. 321
To do simulation, we use centralized version of LPT,
however Espan, EEspan and AEEspan work in distrib-
uted manner. In below figure, to compare performance of
the trees which are constructed by algorithms, we do not
consider transmission and receiving energy for routing
packet that flooded for tree reconstruction. As mentioned
before, nodes send their data via the tree which is con-
structed by the algorithm, so it is important to compare
paths that each algorithm selects to send data to sink.
At the first simulation trial, to evaluate the energy effi-
ciency of proposed algorithm, AEEspan, each node is
assigned with an initial energy that is randomly chosen
between 8J and 20J. After some simulation rounds, we
measure remained energy of network nodes. In Figure 3,
sum of the remained energy of all nodes in network is
plotted versus number of nodes for four algorithms.
Since LPT algorithm selects paths by considering only
energy parameter, nodes transmit their data via longer
paths which make higher energy consumption. In Espan
algorithm, nodes transmit data via shortest paths, but by
failing low power nodes in these paths, data must be
transmitted via other paths which may be longer. While in
EEspan [1] and AEEspan, nodes consume less energy,
because in these algorithms, tree is constructed by apply-
ing a reasonable relation between energy and distance
parameters, Unlike the algorithms given in [4,8] use only
one of these parameters as the main parameter and the
other parameter is used as lower priority parameter.
To verify above claim about path length, we study sug-
gested paths in these algorithms. In the aggregation tree
construction algorithms, average path length parameter
represents average depth of tree that is the number of the
hops between the nodes and the root, so, the tree with
deeper branch means that nodes transmit data via longer
path, and this causes more delay and also more energy
consumption.
In Figure 4, the average path length is plotted versus
the number of nodes. As in AEEspan, automata select
their parents with the highest selection probability, and
this value has converse relation to distance parameter, so
the node with less distance has higher priority to be se-
lected as parent that causes the parent with higher energy
and less distance is selected.
As shown above, LPT tree has longer branches, be-
cause of not regarding distance parameter at all, while in
Espan which regard distance as main parameter, tree has
shorter branches. While in thus work, branches are be-
tween these two bounds.
By considering distributed algorithms, and apply tree
construction cost, consumed energy to transmit and re-
ceive routing packet, we evaluate the performance of
proposed algorithm by considering reconstruction section.
As describe earlier, the algorithm with automata learn-
ing property consumes less energy as a result of prevent
flooding routing packet. By considering learning property,
transmission volume is decreased that leads to more
power saving. To show this, the remaining energy of
network nodes is measured. In Figure 5, sum of the re-
mained energy of all nodes in network is plotted versus
number of nodes.
Figure 3. The remaining energy of algorithms without
considering tree reconstruction cost.
Figure 4. Average hop count to root.
Figure 5. The remaining energy of distributed algorithms
with considerin g tre e reconstruction cost.

322 Z. ESKANDARI ET AL.
Figure 6. Number of alive nodes at N=300.
Figure 7. Number of alive nodes at N=500.
Figure 8. Average lifetime c o mparison.
We measure the number of alive nodes after each
simulation round in Figure 6, 7 when N = 300, and 500
nodes, respectively. As in AEEspan, automata select a
parent with the highest selection probability which has
direct relation to energy parameter, so the nodes with
low energy remain a longer time in the network rather
than the other algorithms.
For example, in Figure 7, three algorithms work simi-
larly by the round 52, but after that, nodes in Espan tree
start to fail sharply, while in AEEspan, nodes failing start
later and in slighter manner.
As mentioned before, energy efficiency is a main goal
of algorithms in wireless sensor networks. By decreasing
energy consumption that led to prevent from failing net-
work nodes, network’s coverage whether spatial or tem-
poral is supported better and network’s lifetime increases.
AEEspan algorithm by decreasing transmission volume,
can meet this goal.
In Figure 8, for these algorithms, the average lifetime
is plotted versus the number of nodes. The results are
obtained after 20 different simulation trials. As seen in
Figure 8, the proposed algorithm has higher lifetime than
other algorithms. Based on lifetime definition, lifetime
has direct relation to alive node numbers.
6. Conclusion
One of the most important limitations of the wireless
sensor networks is the network’s energy. Aggregation
algorithms have a considerable role in decreasing the
energy consumption due to the reduction of the transmit-
ted data volume. Aggregation algorithms construct the
Aggregation tree based on the algorithm parameters, and
determine the transmitting path of the root for each group.
In this paper, the tree construction is presented based on
automata. An automaton is an able-to-learn structure
which tries to choose the best path to send the data to the
root by getting feedback from the environment. Also, by
prevent from flooding routing packet in entire network,
proposed algorithm consume less energy. As the simula-
tion results show, the proposed algorithm has more life-
time and lower energy consumption.
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