Stenier-based Energy Efficient Multicast Routing for Wireless Sensor
Valeri Katerinchuk
and Celal Ozturk
Department of Informatics, King’s College London, Strand Campus, London, U.K.
Department of Computer Engineering, Erciyes University, Kayseri, Turkey
Wireless Sensor Networks, Multicast Routing, Steiner Tree, Sink Mobility.
Wireless Sensor Networks (WSN) consist of a suite of sensor nodes capable of autonomous data collection
and wireless communication deployed over an area of interest. They constitute a popular means of automated
data collection with the sensors working together to form a wireless communication network and funnel col-
lected data to nodes capable of transmitting data to a single or multiple collection points for interpretation.
The routing instance from a single source to multiple destinations is formalized as a Multicast Routing Prob-
lem (MRP). Recent applications WSNs have focused on exploiting sink mobility technology (with multiple
destinations) to extend network lifetime. As the nodes are often reliant on limited power sources, algorithms
for efficient routing of data in these networks have been a source of increased research interest. However, few
current algorithms consider the remaining energy levels of an individual network node during a single routing
instance, creating a situation where the network may become disconnected faster than necessary. In this paper,
we present an algorithm for multicast routing in wireless sensor networks implementing energy-reweighting
techniques to simultaneously optimize the energy-cost of a routing and the network lifetime.
Wireless sensor networks are a popular method of
automated data collection consisting of a series of
sensors distributed over a physical space. The
sensor nodes, which are generally equipped with
data processing and communication capabilities, au-
tonomously collect data about their environment and
cooperate to funnel the data to a single or multiple
collection point nodes. Potential applications of such
networks can be found in the military and medical
fields, in environmental monitoring, in the monitoring
of vehicles and machines, and anywhere else where
spatially distributed collection of data about the en-
vironment is necessary. The individual sensor nodes
employed by such networks are often battery pow-
ered, and therefore with a limited lifetime, making the
conservation of energy within an individual node as
well as over the entire network a relevant issue for the
purpose of data transmission (Ren et al., 2011).
Routing in wireless sensor networks is very chal-
lenging and different to traditional networks due to
characteristics specific to sensor nodes. These are
tightly constrained in terms of transmission power,
on-board energy, processing capacity and storage.
In general, a routing protocol for WSNs needs to
deal with scalability, energy efficiency, robustness, la-
tency, low computation and memory usage. Many
routing mechanisms have been proposed in WSNs
to overcome these challenges; however finding and
maintaining routes in such a way as to minimize en-
ergy expenditure is the most important issue in al-
most all applications of WSNs. To minimize energy
consumption, routing techniques proposed in the lit-
erature employ well-known methodologies specific to
WSNs, such as data aggregation, clustering, differ-
ent node role assignment, and data-centric methods
(Khan et al., 2012) (Kumar and Raj., 2012). All these
routing methods are divided into flat-based routing,
hierarchical-based routing, and location-based rout-
ing depending on the network structure. In flat-based
routing which is considered in this work, all nodes are
assigned equal roles and functionality (Yang and Mo-
hammed, 2010).
The majority of energy aware wireless sensor net-
work routing protocols seek to minimize the total en-
ergy consumption in each routing session to increase
the network lifetime. Most energy-efficient protocols
use algorithms for computing minimum cost paths
with the link metric representing the energy required
Katerinchuk V. and Ozturk C..
Stenier-based Energy Efficient Multicast Routing for Wireless Sensor Networks.
DOI: 10.5220/0005217003460352
In Proceedings of the International Conference on Operations Research and Enterprise Systems (ICORES-2015), pages 346-352
ISBN: 978-989-758-075-8
2015 SCITEPRESS (Science and Technology Publications, Lda.)
to transmit a packet over the link (Chun and Tang,
2006). Research has primarily focused on wireless
sensor network representations with a single or a
small number of static sink nodes. Recently, how-
ever, there has been increased interest in exploiting
mobile sink technologies for WSNs due to the pos-
itive impact these can have on energy conservation
of individual nodes and network lifetime (Friedmann
and Boukhatem, 2007).
Our focus is on energy efficient multicast rout-
ing in wireless sensor networks with multiple desti-
nations, representing mobile sink nodes. In multicast
communication data is delivered to a number of nodes
which are geographically dispersed in a deployment
field and there is no restriction on the boundary for
data transmission. The most popular multicast routing
approaches are based on trees which are constructed
from source nodes to multicast group members. The
computation of a minimum cost multicast tree in
wireless networks is an NP-Hard problem (
et al., 2002). Researchers have proposed numerous
heuristic algorithms for multicast communication in
wireless sensors networks. However, while these al-
gorithms are efficient for some scenarios they may
perform poorly in others (Won and Stoleru, 2011).
Proposed energy-efficient algorithms have fo-
cused primarily on the networks’ application natures
and on optimizing limited capabilities of the sensor
nodes. Most of these algorithms attempt to minimize
the cost of the routing paths aiming to achieve mini-
mum overall energy expenditure in all transmissions
(Feng and Heinzelman, 2009), but in general this aim
does not always significantly help to improve the net-
work lifetime when there is insufficient focus on con-
structing routing trees balancing the minimum total
energy and energy distribution.
(Simek et al., 2008) examine the inherent ineffi-
ciency of existing wireless protocols when adapted
to wireless sensor networks. They proceed to iden-
tify two broad groups of Multicast Routing (MCR)
protocols; blind flooding and geographical, and intro-
duce a number of algorithms for these protocols. The
papers A Node-Weighted Steiner Tree-Based Heuris-
tic (Li et al., 2004) and Energy-Efficient Broadcast
and Multicast Trees for Reliable Wireless Communi-
cation (Banerjee et al., 2003) present a Steiner tree
based approach to MCR in wireless networks trans-
posed directly from algorithms for wired networks.
All these approaches, suffer from the same flaw of
failing to consider the ongoing effect of energy de-
pletion in the network over a number of Multicast re-
quests, even where an individual request may be op-
timal. Indeed, algorithms focusing on finding a mini-
mum cost MCR for this problem will often route over
a subset of favourite edges when run over a number of
consecutive Multicast requests. This results in a dras-
tic decrease of the network’s lifetime as depleted and
overused nodes go offline.
(Cheng et al., 2006) proposed the MWIA algo-
rithm which re-weighted the nodes in each iteration
to reflect the energy depleted and guiding the broad-
cast tree around commonly used edges. The mini-
mum spanning tree, choosen as a solution with the
minimum cost but a larger number of used edges,
compares unfavourably to a Steiner tree in terms of
energy conservation. Furthermore, the adaptation of
the broadcast tree algorithm toward MCR presented
is deterministic, generating an issue of computational
complexity for large networks.
In this work, we present a heuristic approach
for a Steiner tree based algorithm considering the
combined objectives of energy minimisation and ex-
tending the network lifetime by reliable multicast
trees. We aim to propose a hybrid heuristic algorithm
for routing a number of multicast requests through
a wireless sensor network. The algorithm imple-
ments a new, weighted energy function with edges re-
weighted after the routing of each scheduled multicast
request based on the depletion of the energy capacity
of utilised nodes. The aim of the re-weighting is to
guide the search around commonly used nodes where
The WSN is represented as a graph G=(V, E) where
V = m
, m
, .., m
is a set of nodes and E = l
, l
a set of edges, where each edge l connects two nodes
in V . We define an energy cost function Co over E
such that each edge l
in E has an associated cost of
transmitting data over that edge Co(l
). An instance
of a multicast-routing problem is defined as:
m = [s D] (1)
where s V is the source node of m, D = v
, v
, ..v
V is the set of destination nodes. We assume full net-
work knowledge by every sensor node. The MCR for
multiple consecutive multicast routing requests is de-
fined as
[P = G;Co; M], (2)
where M = m
, m
, ..m
and G and Co are as defined
A popular way to model the Multicast Routing Prob-
lem is as a constrained Steiner Tree problem. The
Steiner tree problem in energy-efficient MCR is sum-
marised by finding in a graph G a minimum cost tree
spanning the source and all destination nodes such
that the number of edges is minimized. The Steiner
tree is generally considered superior to the Minimum
Spanning tree for the MCR as the process of also min-
imising the number of used edges reduces unneces-
sary data traversing the network (Novak et al., 2002).
Computing a Steiner Tree was shown to be
NP-Complete in (Karp, 1972) however, there exist a
number of heuristics for its computation. A popular
heuristic approach is the KMB algorithm which
comes within approximately 5% of the optimal. We
use an adaptation of the KMB to generate Steiner
tree based solutions for MCR requests over a dynam-
ically re-weighted network. The KMB adaptation,
for each transmission, works in the following manner:
Starting with the input graph G and a set of steiner
points S (the source and destination nodes).
Constructs a complete undirected distance G1 graph
from G and S. The only nodes in G1 should be modes
listed in S.
Find the minimum spanning tree of G1.
Construct subgraph Gs of G by replacing each edge
in G1 with its corresponding path in G.
Find the minimum spanning tree G2 of Gs.
Construct a Steiner tree T from G2 by deleting edges
so that all leaves are Steiner points.
Definition 1. A Wireless Sensor Network (WSN) is
a number of sensor nodes distributed over a physical
area where the nodes are computational units fitted
with sensors and are capable of data collection and
processing as well as transmitting data wirelessly and
receiving wireless transmissions from other network
Every node in the WSN must be within commu-
nication range of at least one other node in the net-
work. Nodes collect data autonomously and coop-
erate to funnel data toward those sensor nodes capa-
ble of transmitting it to a data repository for analysis,
otherwise known as destination nodes or sink nodes.
Which of the sensor nodes in the network possess this
capability is not fixed in our representation and can
vary with time. All WSN sensor nodes are identi-
cal in every respect including the effective range at
which they can transmit data. All wsn sensor nodes
have a battery to provide power with a limited, identi-
cal amount of available energy before the battery runs
dry and the node goes offline.
Definition 2. An edge between two network nodes l =
, v
) where v
, v
V represents the fact that these
nodes are within effective transmission range and can
The cost of transmitting data is a unit cost by de-
fault as we assume in the current work the amount
of power required to transmit over any edge in E is
identical. This is because in the most common WSN
scenario nodes cannot vary the strength of transmis-
sion and transmit at maximum power to any destina-
tions in range. The amount of energy expended by a
node receiving is negligible compared to the energy
expended transmitting data. Therefore the cost of re-
ceiving in our representation is set to zero.
Definition 3. A multicast request consists of data to
be transmitted from one sensor node to one or more
destination nodes.
Definition 4. A Successful request is a request where
the data is delivered at all destination nodes. A suc-
cessful requests depletes the energy of every node in-
volved in transmitting it by a constant amount (That
is, the source node, all intermediary nodes but no des-
tination nodes).
Definition 5. A Bad request or Unsuccessful request
is a request where data cannot be delivered to ev-
ery destination node (because of network partition-
ing etc.). Such a request is marked as failed and not
transmitted, therefore depleting no energy.
A popular naive solution to the multicast problem
is the routing of requests by generation of a Short-
est Path tree in which the shortest paths from the
source to each individual destination are calculated
and these paths are superimposed to create the multi-
cast tree. While possessing the advantage of ensuring
the speediest delivery to each destination this method
is wasteful of energy potentially creating unnecessary
data duplication in the network by failing to consider
the routing as a whole. A steiner tree based algorithm
deals with this problem by aiming to reduce the num-
ber of edges used and minimising the total energy of
the entire routing. However, current Steiner tree based
algorithms fail to consider the effects of energy deple-
tion, over consecutive runs with individual multicast
requests, of nodes along popular (shorter) paths. This
results in a shorter network lifetime and a speedier
fragmentation of the network.
The energy-efficient MCR for WSNs as the con-
secutive routing of a set of multicast requests over a
network is aimed to maximise the network lifetime by
minimising the usage of energy for each request. The
proposed algorithm takes into account the residual en-
ergy remaining in nodes after each multicast routing
by re-weighting, each edge l
= (v
, v
) to reflect the
energy levels of v
and v
, both of the nodes it con-
nects. The purpose of this function is to increase the
cost of an edge proportionally with the decreasing en-
ergy levels of the nodes it connects in order to en-
courage the algorithm to path around nodes with low
residual energy in future runs, thus extending the net-
work lifetime. The inputs are a randomly generated
network and a randomly generated set of requests. It
uses an adaptation of the popular KMB heuristic ap-
proach to calculate each individual routing. However,
after each routing the cost of any edge connecting one
or more nodes the energy level of which had dimin-
ished during the routing is calculated as:
) =
) + E(v
where C(l
) is the energy cost of the link l
, E
is the maximum energy of a node, E(v
) and E(v
are the current energy levels of nodes v
and v
, re-
(Akyildiz et al., 2002) defined random deployment as
one of the two primary deployment methods of wire-
less sensor networks. We have tested our algorithm
on a set of randomly generated networks consisting
of 100 nodes with 200 edges against a non-energy-
weighted Steiner tree algorithm for multicast rout-
ing, based on the KMB algorithm by following the
methodologies outlined in (Banerjee et al., 2003) and
(Li et al., 2004).
Every node in the network has at least one and at
most 99 neighbors (nodes connected by a link). No
pair of nodes may share more than one link. Nodes
have full knowledge of the network and the routing
algorithm is run in a source node prior to transmis-
sion. Running the routing algorithm and receiving
data from another node cost no energy. Energy cost
is incurred only in transmitting data. Requests which
cannot be transmitted to every destination are not sent
and consume no energy. Both algorithms were given
an identical sequence of randomly generated requests
until the termination condition, the end of the network
lifetime, had been reached. The computational times
for all experiments and all algorithms were very close.
A popular definition for the end of the lifetime of a
network is the time when a node in the network has
no more energy (Chang and Tassiulas, 2004), (Cheng
et al., 2008), (Kang and Poovendran, 2005). Our
initial experiments, therefore, terminated both algo-
rithms when a single node died, with the results pre-
sented in the first row of the Table [1]. The columns
in tables represent:
The total number of requests processed before ter-
The number of these requests which were not
routed successfully.
The total energy remaining in the network (out of
The mean energy remaining in a live node in the
residual network.
The termination condition which must be met for
the algorithm to stop.
Table 1: Energy-Weighted and Non-Energy-
Weighted algorithms results based on dead nodes
termination condition.
1 node 420 0 54 4903 268 0 77 7003
10% 521 13 40 3663 471 57 58 5261
15% 656 111 35 3205 587 123 51 4609
20% 623 90 35 3154 720 243 48 4384
The results for a single node termination con-
dition illustrate the improvement of the Energy-
Weighted KMB based algorithm over the Non-
Energy-Weighted one. The total number of requests
processed successfully was 56% greater than in the
Non-Energy-Weighted instance. There were no un-
successful requests due to the termination condition
used. Moreover, there was a 30% reduction in the
mean energy within a live node in the residual net-
work indicating a more efficient use of resources by
the Energy-Weighted algorithm - with the energy be-
ing an average of 54 in the Energy-Weighted runs and
77 in the Non-Energy-Weighted case.
(Cheng et al., 2008) proposes that in a well designed
network when the first node dies its neighbors will
soon follow from having to take over the strain of the
node, however we have seen that in random networks
the mean energy of a node in the network at the time
of the death of the first node tends to be still over 50%.
Another common definition of the end of a network
lifetime is when a certain percentage of the nodes be-
come non-functional (Chen and Zhao, 2005), (Cheng
et al., 2008). For the next set of tests we compared the
algorithms using termination criteria of varying per-
centage of dead nodes, the results are demonstrated
in the Table [1].
In running the algorithms with a 10% node death
termination criteria we also calculated the shortest
path to each destination node using Djkstra’s algo-
rithm and we noticed that the results for the Non-
Energy-Weighted KMB and Shortest path algorithms
are very similar, with the Shortest path approach be-
ing only slightly worse on average in every respect -
463 requests routed on average with an average mean
energy of 58 and total energy of 5278 in the 10%
nodes dead scenario. The shortest path based algo-
rithm was also significantly worse in terms of unsuc-
cessful requests with an average of 69 bad requests
for the 10% nodes dead scenario. Therefore, we do
not need to run the Shortest Path based algorithm
and will instead keep only the non-energy-Weighted
KMB for comparison in all other experiments. The
Energy-Weigthed algorithm constitutes a significant
improvement on the two previous algorithms, with
around a 10% improvement on the number of pro-
cessed requests with an average 81% reduction in the
number of bad requests. Also indicative was a 32%
reduction in the average energy of a live node in the
residual network indicating that the Energy-Weighted
algorithm was able to make far better use of network
resources prior to the end of the network lifetime.
In the runs missed out from the results of the runs
against a 15% network death termination criteria, the
number of bad requests, as the percentage of dead
nodes required to consider the network dead is in-
creased, becomes an exponential curve. Past a certain
point in the operational life of a WSN it becomes so
disconnected that a successful request is routed very
rarely. The network during the unsuccessful runs had
already crossed this point with a 15% network death
termination criteria. The Energy-Weighted algorithm
processed over 1200 requests of which over half were
unsuccessful, while the Non-Energy weighted algo-
rithm failed to terminate within the requests set (as
unsuccessful requests do not consume energy). It was
ultimately felt that including these runs would skew
the results. The comparative results of the Energy-
Weighted algorithm are maintained, with a 15% im-
provement on the number of requests processed and
a 12% reduction on the number of bad requests com-
pared to the Non-Energy-Weighted algorithm. Con-
sistently, there was a 31% reduction in mean energy
of a live network node.
In the tests against a 20% network death condition
the number of bad requests for both algorithms be-
gins to increase exponentially indicating the increased
partitioning of the network. Nevertheless, even under
these circumstances, the Energy-Weighted algorithm
constitutes a significant improvement over its counter-
part with a consistent 16% improvement on the num-
ber of requests processed and a large 63% reduction
in the number of bad requests. However, at higher
percentages of nodes dead the difference in bad re-
quests becomes significantly less as both networks be-
come disconnected almost entirely and continuously
process requests unsuccessfully. The improvement in
the mean energy of a live node (a 27% reduction) is
consistent with previous results.
We also carried out tests utilising a stopping crite-
ria where a number of consecutive bad requests were
taken as a sign of the end of a network lifetime. Ta-
ble [2] presents the results for 10 and 30 consecutive
bad requests for the Energy-Weighted and the Non-
Energy-Weighted algorithms.
Table 2: Energy-Weighted and Non-Energy-
Weighted algorithms results based on bad requests
termination condition.
10 564 47 39 3492 545 102 54 4864
30 682 148 40 3131 767 288 54 4318
While the consecutive bad request termination cri-
teria halted the algorithm at different points in the net-
work life compared to the former stopping criteria, the
results were, however, consistent. The results for the
10 consecutive bad requests were closer to those for
a less disconnected network such as 10% or 15% net-
work nodes criteria: The improvement by the Energy-
Weighted function on the number of requests pro-
cessed (compared to the Non-Energy-Weighted func-
tion) was a minor 3%, however the reduction in bad
requests was 45.7%. The reduction in mean energy of
a node was 28%. Tests against 30 consecutive bad re-
quests placed the residual network closer to the point
of being totally disconnected. However, with a 12%
improvement on the number of processed requests, a
49% decrease in bad requests and a 26% decrease in
mean energy per live node, the results for the Energy-
Weighted algorithm are consistently superior.
We also ran a series of tests with a termination
criteria based on the percentage of dead edges, which
may more accurately represent the level of partition-
ing of the network, as the death of a highly connected
node may have far more impact than that of an aver-
age node. The results are obtained by having stopping
criteria of 10, 15, 20, 30 and 35 percent of edges dead,
are given in Table [3].
Table 3: Energy-Weighted and Non-Energy-
Weighted algorithms results based on dead edges
termination condition.
10 413 11 5112 56 284 12 6912 76
15 496 24 4121 45 344 24 6317 70
20 527 32 3783 42 412 41 5700 63
30 577 55 3417 37 502 70 4878 54
35 623 86 3191 35 503 70 4867 54
The improvement in the number requests appears
to decrease as the network nears full partitioning,
ranging from 67% to 15%, however as the final value
improved on the previous score raising the improve-
ment to 24% this may indicate that the decrease is
more general, or even a feature of the network, the av-
erage improvement being 35%. The decrease in bad
requests fluctuated wildly and, in fact, in one instance,
for the first time, the Energy-Weighted algorithm per-
formed worse in terms of bad requests than its coun-
terpart with a 23% increase in bad requests. However
the overall performance of the algorithm in this in-
stance was superior with a 24% improvement in the
number of successful requests. The average improve-
ment on the number of bad requests was 7.2%. The
decrease of the mean energy of a node between the
two algorithms fluctuated without pattern and aver-
aged at 32.2% decrease of mean energy per live node
in the Energy-Weighted algorithm compared to the
Non-Energy-Weighted algorithm.
An algorithm for multicast routing in wireless sensor
networks based on energy-reweighting is proposed
to optimize the energy-cost of a routing and the
network lifetime. We have found the proposed
approach, based on re-weighting of edges to reflect
the remaining energy level of the nodes, improves
network lifetime, routing significantly more success-
ful requests before the WSN becomes disconnected,
while utilising the resources of the network far more
effectively. This is represented by a steady decrease
in the average remaining energy of a random, live
node in the network after it is disconnected.
The results of the Energy-Weighted Steiner tree
based approach for the multicast routing problem in
Wireless Sensor Networks were consistently superior
to a purely Steiner tree based algorithm and a Shortest
path based algorithm. The percentage of improve-
ment on the total number of requests processed varied
greatly between runs, being between 3% and 56%
on average, depending on the termination conditions.
The percentage of improvement in this regard seemed
to weakly decrease as the network became more
disconnected with the average improvement over all
experiments being 21%. The reduction in the number
of unsuccessful requests (where applicable) also
fluctuated between 7.2% and 81%. There was even a
single instance where the Energy-Weighted algorithm
performed worse than its counterpart in this regard,
however simultaneously improving significantly on
the number of successful requests. Nevertheless,
there was a generally consistent improvement on the
number of bad requests, with the Energy-Weighted
algorithm averaging out at 43% less bad requests.
The Energy-Weighted algorithm also maintained a
consistent decrease in the mean energy level of a
live residual network node after termination. The
improvement here fluctuated very mildly averaging at
a 29% decrease in energy and indicating a consistent,
significantly more efficient use of network resources
on the part of the Energy-weighted algorithm.
The paper considered identical transmission
costs per node as this is the more common scenario
in actual WSNs, as though the nodes may be at
differenct actual distances from one another, each
node in a common WSn transmits with the same
invariable signal strength. Thus the cost of tranmis-
sion is the same to any node within range regardless
of actual distance. However, if the transmission
costs were different, perhaps under the assumption
of different sensor types in the network, the model
would require bi-directional edge costs, with the costs
varying depending on the transmitting node. This
may be an interesting future extension of the research.
The authors would like to thank Dr. Kathleen
ofel for her support. This work is partially
supported by the Scientific and Technical Research
Council of Turkey and Erciyes University Scientific
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