IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 11, NOVEMBER 2006 2127
Gateway Placement Optimization in Wireless Mesh
Networks With QoS Constraints
Bassam Aoun, Raouf Boutaba, Senior Member, IEEE, Youssef Iraqi, and Gary Kenward
Abstract—In a wireless mesh network (WMN), the traffic is
aggregated and forwarded towards the gateways. Strategically
placing and connecting the gateways to the wired backbone is
critical to the management and efficient operation of a WMN.
In this paper, we address the problem of gateways placement,
consisting in placing a minimum number of gateways such that
quality-of-service (QoS) requirements are satisfied. We propose a
polynomial time near-optimal algorithm which recursively com-
putes minimum weighted Dominating Sets (DS), while consistently
preserving QoS requirements across iterations. We evaluate the
performance of our algorithm using both analysis and simulation,
and show that it outperforms other alternative schemes by com-
paring the number of gateways placed in different scenarios.
Index Terms—Approximation algorithms, clustering, gateways
placement, wireless mesh networks (WMNs).
I. INTRODUCTION
W
IRELESS is well established for narrowband access sys-
tems, but its use for broadband access is relatively new.
Wireless mesh architecture is a first step towards providing high-
bandwidth network coverage. Mesh architecture sustains signal
strength by breaking long distances into a series of shorter hops.
Intermediate nodes not only boost the signal, but cooperatively
make forwarding decisions based on their knowledge of the net-
work. Such architecture provides high network coverage, spec-
tral efficiency, and economic advantage.
Recently, interesting commercial applications of wireless
mesh networks (WMNs) have emerged. One example of such
applications is “community wireless networks” [1], [2]. Sev-
eral vendors have recently offered WMN products. Some of
the most experienced in the business are Nortel [3], Tropos
Networks [4], and BelAir Networks [5].
WMNs have a relatively stable topology except for occa-
sional node failures or additions. Practically all the traffic flows
either to or from a gateway, as opposed to ad hoc networks
where the traffic flows between arbitrary pairs of nodes. Gate-
ways would be connected directly to the fixed network, and
Manuscript received October 1, 2005; revised March 4, 2006 and May 1,
2006. This work was supported in part by Nortel, in part by the Natural Sciences
and Engineering Research Council (NSERC), and in part by Communications
and Information Technology Ontario (CITO).
B. Aoun is at the Department of Computer Science, University of Waterloo,
Waterloo, ON N2L3G1, Canada (e-mail: baoun@uwaterloo.ca).
R. Boutaba is with the David R. Cheriton School of Computer Science, Uni-
versity of Waterloo, Waterloo, ON N2L3G1, Canada (e-mail: rboutaba@bbcr.
uwaterloo.ca).
Y. Iraqi is with the Department of Computer Science, Dhofar University,
Salalah, 211 Oman (e-mail: y_iraqi@du.edu.om).
G. Kenward is with Nortel, Ottawa, ON L6T 5P6 K2H8E9, Canada (e-mail:
gkenward@nortel.com).
Digital Object Identifier 10.1109/JSAC.2006.881606
therefore constitute traffic sinks and sources to WMNs. There-
fore, strategically placing and connecting the gateways to the
wired backbone is critical to the management and efficient op-
eration of a WMN.
The analysis of WMN scalability is based on the following
scaling relationships: traffic increases with the number of nodes,
and traffic also increases with the distance over which each node
wishes to communicate (i.e., due to packet forwarding). In [6],
Li
et al. showed that
, the capacity available to each node (i.e.,
the rate at which packets are originated), is bounded by
where is the total one-hop capacity of the network, is the
number of nodes,
is the expected path length, and is the fixed
radio transmission range such that
is the minimum number
of hops to deliver packets.
The above inequality shows that as the expected path length
increases, the bandwidth available for each node to originate
packets decreases. Therefore, the network scales better when the
traffic pattern is local. That is, each node sends only to nearby
gateways within a fixed radius, independent of the network size.
The expected path length clearly remains constant as the net-
work size grows. Hence, for optimal performance, the WMN
should be divided into disjoint clusters, covering all nodes in
the network. Within each cluster, the clusterhead would serve
as the gateway, connected to the wired backbone.
A tree-based routing scheme would easily allow flows aggre-
gation and would minimize overhead, ensuring an optimal uti-
lization of bandwidth [7]. Hence, a spanning tree rooted at the
gateway can be used for traffic forwarding. Each node is mainly
associated to one tree, and would attach to another tree as an
alternative route in case of path failure.
For operational considerations, the gateway placement
problem should take into account the quality-of-service (QoS)
requirements such as delay and bandwidth. In a multihop net-
work, significant delay occurs at each hop due to contention for
the wireless channel, packets processing, and queueing delay.
The delay is therefore a function of the number of communi-
cation hops between the source and the gateway. The delay
constraint is translated into an upper bound
on the cluster
radius, or a maximum depth
of the spanning tree rooted at
the gateway.
Bandwidth requirements are of two forms. First, the total
traffic inside each cluster is bounded by the capacity of the
gateway, based on its connectivity to the internet and its pro-
cessing speed. This requirement is translated into an upper
0733-8716/$20.00 © 2006 IEEE
2128 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 11, NOVEMBER 2006
bound on the cluster size , assuming each AP generates an
equal amount of one unit of traffic.
Guaranteeing a throughput for individual flows in a multihop
wireless network is more challenging. For convenience, we as-
sume a multichannel WMN where interfering wireless links op-
erate on different channels, enabling multiple parallel transmis-
sions. The bottleneck on throughput is therefore reduced to the
load of congested intermediate wireless links. Since trafficis
aggregated and forwarded by intermediate APs, we refer to the
load on individual wireless links as relay load L in unit of traffic.
Therefore, the throughput requirement is translated to an upper
bound on the relay load equal to the capacity of individual wire-
less links in unit of traffic.
In this paper, we address the problem of gateway placement
in a WMN, aiming at placing a minimum number of gateways,
while ensuring the QoS requirements discussed above. We
present a polynomial time near-optimal algorithm to divide the
WMN into clusters of bounded radius under relay load and
cluster size constraints.
The contribution of this work is the design of a novel algo-
rithm consisting of recursively computing minimum weighted
dominating sets (DSs) for placing gateways in a WMN, while
ensuring the above QoS requirements.
The rest of this paper is organized as follows. Section II
presents an overview of related works. Section III describes
the network model, presents the gateway placement problem,
and provides its integer linear programming (ILP) formulation.
Section IV presents a detailed description and analysis of the
recursive DS algorithm with QoS constraints. Experimental
analyses and comparison to alternative approaches are per-
formed in Section V. Section VI concludes this paper.
II. R
ELATED
WORK
Our work inherits two major concepts from the literature: the
capacity facility location problem (CFLP), and clustering and
hierarchical routing in ad hoc networks.
The gateway placement problem could be considered as an
instance of the more general CFLP problem which has been
studied in the fields of operations research and approximation
algorithms. In the past several years, a lot of work has been
done on the design and analysis of approximation algorithms
[8] for two facility location problems: the uncapacitated facility
location problem [9], and the k-median problem [10]. In those
techniques, distance is expressed in terms of Euclidean-distance
(relying on the triangular inequality) rather than in terms of hop-
count, and consequently, an upper bound on the relay load is not
considered. In addition, there is no abstraction of a cluster or
constraints on the cluster radius which is a necessary factor in
placing gateways.
There have been numerous studies on designing hierarchical
routing architectures for ad hoc networks. Routing, based on
a connected dominating set (CDS) forming a spine to relay
routing information and data packets, is a typical technique in
MANETs [11]–[13]. The approximation algorithms developed
to solve the CDS problem are not suitable in our context:
simply relaxing the problem of connecting clusterheads leads
to nonoptimal solutions. In addition, the proposed schemes are
concerned with one-hop clustering, which defeats the purpose
of WMN.
Other works have proposed
-hop clustering algorithms [14],
[15] but none of them satisfy all the requirements of our clus-
tering problem and rarely present a guarantee in comparison to
the optimal performance.
To date and to the best of our knowledge, very few schemes
have been proposed to integrate the WMN with the wired
backbone.
In [16], Wong et al. addressed the gateway placement
problem in two separate settings: either minimizing commu-
nication delay or minimizing communication cost. For each
setting, they propose different statistically tuned heuristics,
using the same strategy: at each step they decide which of the
candidate gateways will be eliminated from further consider-
ation. QoS constraints in terms of bounds on the relay load
and cluster size are not considered. Furthermore, the proposed
approximation algorithm gives no guarantee on the optimality
of the solution. The additional QoS constraints considered in
this paper make the problem more challenging.
In [17], Chandra et al. addressed the problem of gateway
placement, aiming at minimizing the number of gateways, while
guaranteeing AP’s bandwidth requirements. They considered
the problem as an instance of the network flow problem,
allowing multipath routing. However, when constraints on
communication path length are imposed, the proposed greedy
heuristics leads to nonoptimal solutions, and hence no guar-
antee on performance. In addition, the iterative greedy approach
makes the load of the gateways unbalanced, since gateways are
placed whenever others are fully served. Finally, a clustered
view of the WMN is not considered, making the design less
suitable to our context.
The most relevant work to ours is the one in [18]. Bejerano
successfully adopts a clustered view of the WMN and used
a spanning tree rooted at each clusterhead (i.e., gateway) for
message delivery. Bejerano breaks the problem of clustering
and ensuring QoS into two subproblems. The first one seeks
to find a minimal number of disjoint clusters containing all
the nodes subject to an upper bound on clusters’ radius. The
second one considers placing a spanning tree in each cluster,
and clusters that violate the relay load or cluster size constraints
are further subdivided. In this paper, we consider the combined
problem, where the spanning tree and cluster coverage evolve
in parallel as long as QoS requirements are satisfied. We show
that the number of gateways required by our algorithm, subject
to the same QoS requirements, is reduced by almost 1/2 in
some cases, thus leading to a significant saving in deployment
cost.
III. S
YSTEM DESCRIPTION
A. Network Model
We consider the problem of gateway placement in the con-
text of WMN. A WMN is represented by an undirected graph
, called a connectivity graph. Each node repre-
sents an Access Point (AP) with a circular transmission range
of 1 unit. The neighborhood of
, denoted by , is the set of
AOUN et al.: GATEWAY PLACEMENT OPTIMIZATION IN WIRELESS MESH NETWORKS WITH QOS CONSTRAINTS 2129
nodes residing in its transmission range. A bidirectional wire-
less link exists between
and every neighbor and
is represented by an edge
. The number of neigh-
bors of a vertex
is called the degree of , denoted by .
The maximum degree in a graph
is called the graph degree
.
The distance, denoted by
, between two nodes and
is the minimum number of hops between them. The radius
of a node
in is the maximum distance between
and any other node. The radius of is hence defined as the
minimum radius in the graph. On the other hand, the diameter
of
is the maximum distance between two arbitrary nodes (or
the maximum radius).
For computational purposes, we use an adjacency matrix
to represent the connectivity graph. The adjacency matrix of
is a matrix with rows and columns labeled by the
graph vertices
, with a 1 or 0 in position according
to whether
and are directly connected or not. For the
undirected graph
, the adjacency matrix is symmetric.
B. Problem Description
In this paper, we address the efficient integration of the WMN
with the wired network for Internet access, while ensuring QoS
requirements. This consists in logically dividing the WMN into
a set of disjoint clusters, covering all the nodes in the network.
In each cluster, a node would serve as a gateway, connected
directly to the wired network, and serving the nodes inside the
cluster.
In each cluster, a spanning tree rooted at the gateway is used
for traffic aggregation and forwarding. Each node is mainly as-
sociated to one tree, and would attach to another tree as an al-
ternative route in case of path failure.
For operational reasons, the gateway placement or clustering
problem is subject to QoS constraints. As discussed earlier,
the QoS constraints are translated into the following: an upper
bound
on the cluster radius, an upper bound on the cluster
size, and an upper bound
on relay traffic. The gateway
placement problem therefore consists in logically dividing the
WMN into a minimum number of disjoint clusters that cover
all nodes and satisfy all three QoS constraints.
C. ILP Formulation
We formulate the placement problem as an ILP. Let
be the set of APs and be the set of gateways. is a
subset of
as is the case in Nortel solution [3]. We introduce
a binary variable
to indicate whether a gateway is set
up. To represent gateways allocation for APs, we define another
binary variable
which takes the value of 1 whenever AP
is assigned to gateway . represents the min-
imum number of hops between AP
and gateway .
is a binary variable indicating whether the path from to
passes through node . Recall that and are upper bounds
on the relay load and cluster size constraints, respectively. Our
objective function is formulated as follows:
Subject to
Condition (a) denotes that each AP is assigned to one and
only one gateway. Inequality (b) implies that a gateway has to
be set up before being assigned APs. Inequality (c) ensures that
there exists a path with at most
hops between the AP and
the assigned gateway. This constraint implies that a cluster of
bounded radius can be formed. Inequalities (d) and (e) provide
an upper bound on the relay load and cluster size constraints,
respectively. The last three conditions indicate that
, and
are binary variables.
By reducing the minimum set cover problem to the gateway
placement problem given by the ILP above, one can show that it
is NP-hard to find a minimum number of gateways. In practice,
an LP solver, such as Matlab or CPLEX, can only handle small-
sized networks under the proposed model due to the fast increase
in the number of variables and constraints with the network size.
It will not be possible to solve the ILP for large networks due to
memory constraints.
In the next section, we present a polynomial time near-op-
timal approximation algorithm to solve the placement problem
that ensures the QoS requirements.
IV. R
ECURSIVE DOMINATING SET
ALGORITHM
A. Dominating Set Problem
The core algorithm consists of recursive approximations of
the minimum DS problem. The corresponding decision problem
of DS generalizes the NP-hard Vertex Cover problem, and is
therefore also NP-hard [19].
Since the minimum DS problem is NP-hard, we rely on a
greedy approach for approximation. Approximating a DS using
the greedy approach was first proposed by Chvatal [19] for a
more general model. The DS problem could be formulated as
follows.
Definition 1: A DS of a graph
is a subset
of the nodes such that for all nodes , either or a
neighbor
of is in .
2130 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 11, NOVEMBER 2006
B. Algorithm Description
Our algorithm consists of recursively computing minimum
DSs: at iteration
1
, we compute a minimum DS of the graph
resulting from the previous iteration.
Algorithm 1: Recursive DS
1.
2.
3.
4. While
5.
6.
7. Build\_tree
8. if Satisfy QoS
9.
10.
11.
12. else
13. //Restricting the neighbors of
in
14. //such that does not occur again
15. Modify
adjacency matrix
16. end
17. end
18. if Cluster
radius
19. return
20. end
21. return Recursive
DS
The proposed algorithm, Recursive DS , per-
forms recursive calls. At each iteration,
represents the DS of
the previous iterations,
represents the iteration number, and
, and represent the upper bounds on cluster radius, relay
load, and cluster size, respectively.
As shown at line 1, we first compute the adjacency matrix of
graph
, which is an internal representation of the
connectivity graph
consisting of the DS of the previous
iteration
. At iteration , two nodes and are
adjacent if they are
hops away. The rationale is presented in
the next section.
The While loop from line 4 to 17 selects iteratively the node
that covers the greatest number of remaining nodes that
are uncovered in
. The algorithm works as follows. The set
contains, at each stage, the set of remaining uncovered nodes.
The set
contains the cover being constructed (i.e., the dom-
inating nodes). Line 5 represents the greedy decision-making
step. A node
is chosen that covers as many uncovered nodes
1
In this paper, iterations refer to recursive iterations. For example, iteration i
refers to the ith recursive step, or recursion.
as possible (with ties broken arbitrarily). Line 6 shows the re-
sulting subset
composed of and its neighbours. After is
selected, the nodes in
are removed from , and is placed
in
(line 9 and 10). When the algorithm terminates, the set
contains the set of dominating nodes at level .
Lines 18–20 constitute the stopping criteria of the recursive
calls. If the cluster radius of the next iteration is larger than ,
we return the set
which constitutes the set of required gate-
ways, satisfying the QoS requirements. Otherwise, we call the
function Recursive
DS , where would repre-
sent
for the iteration .
However, before proceeding and adding
to the list of domi-
nating nodes, we check whether a cluster rooted at
, including
,isfeasible. Recall that the original network is represented by
and clustering constraints in term of and
should be applied to . We note that each node indexes
(i.e., remembers) all the nodes in
it covered in previous it-
erations, those nodes shall be referred to as cover
; such that
.
We refer to a cluster as feasible if a spanning tree, rooted at
and covering all nodes in cover , satisfies the relay load
and cluster size constraints. At line 7, we build a spanning tree,
and we check if the constraints are satisfied, at line 8. If they
are satisfied, we add
to the list of dominating nodes , and
remove
from . Otherwise, the cover is too large and
we remove an edge from
between and another neighbor in
by modifying Adj such that the combination of does not
occur again. This approach gives the chance to different feasible
clusters to form before moving to the next iteration and increases
the coverage of clusters. Hence, whenever the cluster radius
reaches the upper bound
, all the clusters are guaranteed to
satisfy the cluster size and relay load constraints.
Determining feasibility before reaching the maximum ra-
dius size provides flexibility in terms of reclustering with
neighboring nodes at intermediate iterations. We will show in
Section V that this approach leads to a much lower number of
required gateways, compared to other schemes which check for
the cluster size and relay load constraints after forming clusters
of radius
.
C. Algorithm Illustration
In this section, we illustrate the above algorithm by showing
its intermediate steps. We consider a random topology con-
sisting of 93 nodes in an area of 15
15, as shown in Fig. 1.
The algorithm is implemented in Matlab. The goal is to divide
the network into a minimum number of disjoint clusters subject
to an upper bound on the radius
. Relay load and cluster
size constraints are relaxed for the sake of simplicity.
The first iteration consists in finding a minimal DS over
. Fig. 2 shows the 22 clusters, , resulting from the
first iteration. The index at each clusterhead represents the order
chosen by the greedy algorithm at line 5. The order reflects
the idea of selecting the nodes which can cover a maximum
number of uncovered nodes first. We note that the number of
nodes
moving to the next iteration is considerably
lower than the original
.
AOUN et al.: GATEWAY PLACEMENT OPTIMIZATION IN WIRELESS MESH NETWORKS WITH QOS CONSTRAINTS 2131
Fig. 1. Original network consisting of 93 nodes. We aim to place a minimum
number of gateways satisfying the cluster radius
R
=6
constraint.
Fig. 2. The resulting clusterheads constitute
V
, as a result of the first iteration.
This consists of minimal DS over
G
(
V;E
)
of Fig. 1.
Fig. 3 shows the graph . Recall that two vertices
in
are connected if they are two hops away in the original
network
. The indices at each in Fig. 3 represent the
weight computed by the greedy algorithm, at line 5, which is the
degree of the node observed in Fig. 2, and consequently shows
the order in which they were selected.
Fig. 4 consists of finding a minimal DS
over
shown in Fig. 3. The index at each clusterhead shows the order in
which
were selected. Fig. 5 shows the resulting graph
. Since any two nodes in are at least three-hops
away, an edge
exists if and are
three-hops away. Finally, Fig. 6 shows the resulting
at the
third iteration. The algorithm stops since the cluster radius of
the next iteration exceeds the upper bound
. The next section
will present an analytical analysis of the algorithm, formulating
the relation between the maximum cluster radius
and iteration
Fig. 3. The graph
G
(
V ;E
)
.
Fig. 4. The clusterheads constitute
V
as a result of the second iteration. It
consists of a minimal DS over
G
(
V ;E
)
of Fig. 3.
Fig. 5. The graph
G
(
V ;E
)
.
