Stenier-based Energy Efﬁcient Multicast Routing for Wireless Sensor

Networks

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

Keywords:

Wireless Sensor Networks, Multicast Routing, Steiner Tree, Sink Mobility.

Abstract:

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.

1 INTRODUCTION

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

346

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 (

Cagalj

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

possible.

2 METHODOLOGY

The WSN is represented as a graph G=(V, E) where

V = m

, m

, .., m

is a set of nodes and E = l

, 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

above.

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

Stenier-basedEnergyEfficientMulticastRoutingforWirelessSensorNetworks

347

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

nodes.

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

communicate.

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

ICORES2015-InternationalConferenceonOperationsResearchandEnterpriseSystems

348

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:

C(l

) =

max

E(v

) + E(v

)

(3)

where C(l

) is the energy cost of the link l

, E

max

is the maximum energy of a node, E(v

) and E(v

)

are the current energy levels of nodes v

and v

, re-

spectively.

3 EXPERIMENTAL RESULTS

(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-

mination.

The number of these requests which were not

routed successfully.

The total energy remaining in the network (out of

10,000).

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.

EW NonEW

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-

Stenier-basedEnergyEfficientMulticastRoutingforWirelessSensorNetworks

349

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.

EW NonEW

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.

EW NonEW

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,

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350

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.

4 CONCLUSION

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.

ACKNOWLEDGEMENTS

The authors would like to thank Dr. Kathleen

Steinh

ofel for her support. This work is partially

supported by the Scientiﬁc and Technical Research

Council of Turkey and Erciyes University Scientiﬁc

Research Projects, Project No: FBA-12-4029.

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