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An Efficient and Minimum Cost Topology Construction for Rural Wireless Mesh Networks


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									                                        (IJCSIS) International Journal of Computer Science and Information Security,
                                        Vol. 8, No. 6, September 2010

     An Efficient and Minimum Cost Topology Construction for Rural Wireless Mesh
                          Prof. V. Anuratha & Dr. P. Sivaprakasam
Abstract                                               is rural and are on the wrong side of the
                                                       digital divide.
Many research efforts as well as
deployments have chosen IEEE802.11 as a                Bridging this divide necessitates, providing
low-cost, long-distance access technology to           internet connectivity to each and every
bridge the digital divide. IEEE 802.11 Wi-Fi           village. Providing the same by expanding
equipment based wireless mesh networks                 the current telephone network to rural areas
have recently been proposed as an                      is infeasible because of the huge initial
inexpensive approach to connect far-flung              infrastructure costs. Also, deployment of
rural areas. To establish such network high-           cellular wireless would not be sustainable
gain directional antennas are used to achieve          because of its business model, which
long-distance wireless point-to-point links.           demands more high-paying consumer
Some nodes in the network are called                   density.
gateway nodes and are directly connected to
the wired internet, and the remaining nodes            Emerging      technologies    like    802.16
connect to the gateway(s) using one or more            WMAN[12],[13], have not yet reached the
hops.                                                  scale of competitive mass production, hence
                                                       the equipments are expensive. In this regard,
In this paper the cost of constructing the             the 802.11 Wi-Fi has shown tremendous
antenna towers required is investigated. The           growth and acceptance as a last hop access
problem is NP hard is shown and that a                 solution, because of their low price.
better than O(log n) approximation cannot              Although 802.11 was primarily designed for
be expected, where n is the number of                  indoor operation, but [3] has established the
vertices in the graph. To minimize the                 possibility of using 802.11 in long-distance
construction cost a new algorithm is                   networking.
proposed called constant time approximation
algorithm.                                              The diverse requirements are in provisions
                                                       of 1) Communication pattern which deals
The results of proposed approximation                  with the mode of communication one-to-
algorithm are compared with both the                   one, one to- many, many-to-one, and many-
optimal solution, and a naive heuristic.               to-many, 2) Delay (real-time, non-real-time,
                                                       and delay-tolerant), 3) Service availability
INTRODUCTION                                           (centralized, distributed, and location-aware)
                                                       that deals with the awareness of the
There has been a huge proliferation of
                                                       availability of different services, such as
Internet and other communication based
                                                       Internet access, real-time communications,
services in the last two decades. However,
                                                       content distribution, interactive gaming,
this spread is confined to developed
                                                       medical applications, and vehicular safety
countries, and metropolitan pockets of
                                                       applications. 4) Security and 5) Reliability.
developing countries. This is really
                                                       An essential requirement to establish long-
unfortunate for developing countries like
                                                       distance links is that line-of-sight is
India, where around 74% of the population
                                                       maintained between the radio antennas at the

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                                                                                   ISSN 1947-5500
                                         (IJCSIS) International Journal of Computer Science and Information Security,
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To ensure line-of-sight across such long                on the most critical design issues in
distances would require the antennas to be              multihop wireless networks. Topology
mounted on tall towers. The required height             control has been investigated extensively in
of the towers depends both on the length of             the literature. Nevertheless, it is noted that
the link, and the height of the obstructions            most existing studies do not consider the
along the link.                                         requirements on upper layer applications or
                                                        services. In this article the author address the
        The cost of the tower depends on its            topology control issues on service-oriented
height and the type of material used. For               wireless mesh networks. In particular, the
relatively short heights (10- 20 meters)                author provides a comprehensive survey of
antenna masts are sufficient. For greater               existing works on topology control from a
heights, sturdier and much more expensive               service-oriented perspective. A general
antenna towers are required. In this paper,             framework for topology control in service-
several important contributions are made                oriented     WMNs         is    proposed.     To
towards developing efficient algorithms [14]            demonstrate the effectiveness of the
to solve this problem. First, the requirements          framework, a case study is conducted in
to establish a point-to-point 802.11 link               which the main objective is to maximize the
between two nodes of a given network graph              overall throughput in a network with random
is described. Then the formal definition of             unicast traffic. The performance of this
the Topology Construction problem (denote               topology control scheme is evaluated by
by TC) is given. It’s proved that the problem           numerical results. In addition, it is illustrated
to be NP hard by a reduction from the set-              that the generated topology can support
cover problem.The approximation algorithm               advanced technologies, including network
is presented for this NP hard problem and               coding and physical-layer network coding,
the establishment cost of the tower in rural            which can significantly improve the
areas using constant time approximation                 throughput capacity of a network. The cost
algorithm is presented. The rest of this paper          of laying wire to rural areas is prohibitively
is organized as the following. Section II               expensive.
gives the Related Works of this technique is
presented. In Section III, the Methodology              Also, traditional wireless technologies such
of proposed approach is given. Section IV               as cellular data networks (e.g., EV-DO) and
has the Experiment Results and this paper is            upcoming technologies like IEEE 802.16
concluded in Section V.                                 WiMAX have prohibitively expensive
                                                        equipment costs. As a result, there has been
RELATED WORKS                                           considerable recent interest [6], [7], [8] in
                                                        the design of rural mesh networks using
802.11-based long-distance networks have
                                                        IEEE 802.11 (Wi-Fi) equipment. The cost of
been proposed as a cost-effective option to
                                                        an 802.11 radio (»$50/PCMCIA card) is
provide Internet connectivity to rural areas
                                                        orders of magnitude less than that of
in developing regions, to enable Information
                                                        cellular/WiMAX base stations. Thus, this
and Communication Technology (ICT)
                                                        approach is an attractive option for building
services [5].
                                                        low cost networks. D. S. Lun et.al,[9]
Rural areas (especially in developing                   presented a distributed random linear
regions) have populations with very low                 network coding approach for transmission
paying capacities. Hence, a major factor in             and compression of information in general
network deployment is the cost of the                   multisource multicast networks.
infrastructure and the network equipment. In
                                                        Network nodes independently and randomly
this context, efficient algorithms are
                                                        select linear mappings from inputs onto
investigated for the minimum cost topology
                                                        output links over some field. The author
construction problem in rural wireless mesh
                                                        shows that this achieves capacity with
networks. R. Ramanathan et.al,[4] discussed

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probability exponentially approaching 1                determined by an elliptical area between u
with the code length. Random linear coding             and v termed the first Fresnel zone. To
is     demonstrated       which     performs           establish RF line-of-sight, a significant area
compression when necessary in a network,               of the Fresnel zone (> 60% of the radius of
generalizing error exponents for linear                the Fresnel zone at the location of the
Slepian-Wolf coding in a natural way.                  obstruction [1]) should also clear all
Benefits of this approach are decentralized            obstructions between u and v. However, this
operation and robustness to network changes            can be simply modeled by extending the
or link failures. The author shows that this           height of the obstruction to include the
approach can take advantage of redundant               radius of the Fresnel zone that has to be in
network capacity for improved success                  the clear.
probability and robustness. Some potential
advantages of random linear network coding
are illustrated over routing in two examples
of practical scenarios: distributed network
operation and networks with dynamically
varying connections. The derivation result
also yields a new bound on required field
size for centralized network coding on
general multicast networks.
       In this paper a Novel Topology
Control Scheme is used to identify a set of
semi-permanent highways, such that the best                  Figure1: Computing the height of towers
throughput capacity of the network can be                         at the end-points of a link
obtained. Particularly, the wireless highways               In reality, there can be multiple
are predicted to be rather similar to the              obstructions between u and v. As in Figure
highway system in public transportation                4b, consider multiple obstructions, O1, O2,
system, which can efficiently provide                  …,Ok between u and v. Now, let h(u) and
connectivity in real application.                      h(v) represent the tower heights at the nodes
    A. Computing tower heights at the end-             of u and v. Covering edge (u,v) requires a
        points of a link                               visual and RF line-of-sight connection
    Consider two nodes, u and v that are               between the towers at its two terminal
separated by a distance luv. The edge (u; v)           nodes. This would imply that the straight
is considered to be covered if an 802.11               line fuv joining the top of the two towers (of
based point-to-point communication link can            heights h(u) at u and h(v) at v) should clear
be established between u and v. Assume that            every obstruction in (u,v). Hence, it is noted
the transmit powers [15] and the gains of the          that given a particular pair of tower heights
antennas at both ends are sufficient to over           at u and v, deciding whether these heights
come the free-space path loss between the              covers edge (u,v) can be done in time linear
two points. The first basic requirement to             in the number of obstructions on that edge.2
cover the edge between u and v is that there               B. Modeling tower costs
is a clear visual line-of-sight between the            An important component in this problem is
antennas at the end-points (as shown in Fig.           the nature of the cost function that maps
4a). In other words, the line joining the              tower heights to the cost of building the
antennas mounted on the towers should clear            tower.
any obstructions along the path. Secondly, it
is also required that RF line-of-sight is
maintained between the two points. This is
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                                                                                   ISSN 1947-5500
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                                           Vol. 8, No. 6, September 2010

There are two types of antenna towers that                of the above properties. In the remainder of
are used. For heights less than 20 meters,                this paper, when the height function h is
one can use the cheaper masts. For greater                unambiguous, often the cost of the tower is
heights, the more expensive steel towers is               denoted at a node v as c(v) rather than
used.                                                     c(h(v)).
Further, there is an order of magnitude                       C. The Topology Control Scheme
difference between the cost of the cheaper                    In this framework, it is considered that
masts and that of the steel towers. Thus,                 the highways can be partitioned into two
roughly speaking, the cost function is                    groups, horizontal and vertical. Highways in
constant as long as the cheaper masts can be              each group can operate simultaneously
used and becomes linear in height once the                because they are mutually parallel and can
steel towers are needed, with a jump in cost              be placed away enough to reduce
when we switch from masts to steel towers.                interference below a certain threshold.
                                                          Consequently, horizontal and vertical
Let us denote the height at which the                     highways will partition the whole
material of the tower has to be switched as               geographical area into grids, in which nodes
hmin.                                                     will try to forward their traffic to the nodes
                                                          on neighboring highways. The combination
Further, there is a physical restriction on the
                                                          of the following parameters can be
maximum possible height of a tower,
                                                          considered for the Topology Control
denoted by hmax. Thus, the cost function c
can be formally defined as
                                                               1) Transmission range: Transmission
                                                                    range of each node in the network
                                                                    is traditionally an important
    Where A, B and K are constants and                              design parameter in topology
Ahmin + B >> K. Although, in practice, the                          control. In general, a smaller
cost function can be modeled as discussed                           transmission range will improve
above, our algorithm works with a much                              the channel reuse but may
more general cost functions. Specifically,                          compromise the connectivity. A
we only require the cost function c to satisfy                      larger transmission range will
the following two natural properties C1 and                         improve the connectivity but
C2. C1                                                              reduce      the   channel    reuse.
                                                                    Therefore, an appropriate range is
    Given the tower costs at two neighboring                        chosen as a trade-off between
nodes u and v, it can be determined (in                             connectivity and channel reuse.
polynomial time) whether the corresponding                     2) Type of antenna: When directional
tower heights cover the edge (u,v). This                            antenna or beam forming is used it
simply requires that the corresponding tower                        may improve the capacity of the
height can be computed (in polynomial                               network       by   reducing     the
time) given the tower cost. As mentioned                            interference and improve the
earlier, determining whether the height of                          transmission quality.
the towers is sufficient to cover an edge can                  3) Traffic pattern: Traffic pattern is
be done in polynomial time.C2 the cost                              very important parameter to the
function is monotonically increasing with                           topology.      In   most    studies
height, i.e., h1≥ h2 and c(h1) ≥ c(h2) for                          previously done suggest that the
any values of h1 and h2.                                            traffic is broadcast. With such an
                                                                    assumption, the problem is
    It is easy to verify that the cost function                     formulated in a way such that the
c defined earlier in this section satisfies both                    overall transmission for each

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                                                                                      ISSN 1947-5500
                                              (IJCSIS) International Journal of Computer Science and Information Security,
                                              Vol. 8, No. 6, September 2010

         message is minimized. However,                For the first step of this study, only
         broadcast traffic may only be a               omnidirectional antenna and purely
         special case in the future service-           random unicast traffic pattern are
         oriented WMN, in which a variety              considered. Moreover, the random
         of patterns may appear, from one-             wireless network elaborated to gain
         to one to many-to-many [10].                  insights for the future investigation.
     4) Quality of service (QoS): To
         achieve an efficient network a
         crucial issue is to enable services
         with certain QoS requirements,
         such as bandwidth, delay, security
         and reliability.
                        Figure 2: Approximation algorithm for NP-hard problem










15. Mark all unlabeled vertices of   with label   else (i.e.,




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EXPERIMENTAL RESULTS                                        Given a set of links to be covered, the
                                                        height assignment problem is formulated as
        In this section, extensive numerical            a simple LP, and compute the heights
simulations are carried out to evaluate our             required on every node.
approximation algorithm with the optimal
solution and also a naive heuristic. For this
simulations, synthetic topologies are
generated that aim to match the geographical                 C. Comparing with the naive heuristic
structure of village clusters. Simulation
setup is described in more detail as follows.
                                                        Now the naive heuristic described above is
   A. Generating        synthetic       graph           compared with the proposed approximation
      topologies.                                       algorithm. Graphs considered with number
                                                        of nodes n =10, 15, 20,…, 50. For each
                                                        value of n we generate 50 graph instances.
    A circular plane is considered with a               For each graph, Cnaive the cost of the
radius of 25Kms. Nodes are placed at                    solution produced by the naive heuristic, and
random locations on this plane. A link (u,v)            Capprox cost of the approximation
is considered between any two nodes, u and              algorithm is computed. With this value it is
v, and for these simulations, assume just one           observed that the proposed approximation
obstacle, ouv, located on the middle of this            algorithm performs substantially better than
link.                                                   the naive heuristic.
    The height of the obstruction (ho) is               On average, the solutions returned by the
selected randomly with a maximum value of               naive heuristic range from 60% (for n = 10)
20 meters - the typical height of trees and             to as much as 225% more expensive (for n =
small houses in a rural setting. A weight               50) compared to the solution returned by the
wuv is assigned to the link equal to twice the          naive algorithm.
effective height of the obstruction on this
link. As described earlier, the effective                    D. Comparing with the optimal solution
height of an obstruction, is the sum of the
physical height (ho) and 60% of rf , the
                                                            The optimal solution is computed by
radius of the fresnel zone.
                                                        solving an ILP that models the topology
                                                        construction problem. The CPLEX LP-
                                                        solver [11] to solve this ILP. This approach
   B. Naive heuristic                                   is,    however,     computationally     very
                                                        expensive, and the LP-solver could return
                                                        solutions for graphs with at most 11 nodes.
    In order to compare with the proposed
approximation algorithms, a naive heuristic                 The    solution     returned   by our
is described for selecting connected                    approximation algorithm is compared with
subgraphs and assigning heights to the                  the optimal solution for graphs with number
nodes. As a first step, to select a connected           of nodes n = 8, 9, 10, 11.               For
subgraph of an input graph G, the heuristic             each value of n we generate 50 graphs. For
computes the minimum spanning tree                      each graph Capprox, the cost of the solution
(MST), T of G (using the link weights                   returned by proposed approximation
computed as described above). Next, the                 algorithm, and Copt, the cost of the optimal
heuristic has to assign heights to the nodes            solution.
in G, so as to cover all the edges in T while
minimizing the total cost.

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    Then the mean and standard deviation is                open research problems in the topology
computed over all graphs for different                     construction.
values of n                    .
                                                                   One immediate problem is to
                                                           consider the case of k ≥ 2 vertex or edge
          n           Mean (std. dev.) of                  connectivity, similar to the power optimal
                            Ropt                           network construction for k-connectivity.
          8               0.58 (0.30)                      Another important research direction is the
          9                 0.57 (0.25)                    geometric version of this problem. In
                                                           practice, all nodes within a certain distance
          10                0.55 (0.23)                    of each other can establish a link.
          11                0.52 (0.25)
                                                                    In this paper,          the    location of the
    Table1: New Approximation algorithm                    towers is assumed to              be    fixed (within a
          vs. Optimal Solution.                            village). A variant of           the     problem would
                                                           make the location of              the    tower to be a
    The results presented in Table 7 show
that the incorporated approximation
algorithm gives solutions that are 50 - 60%                        This method has added flexibility
more expensive than the optimal solution                   than the previous method which would
(for small values of n). Thus, the new                     result in reduced cost. The numerical
approximation algorithm performs much                      experiments demonstrate that the proposed
better than the worst case guarantee of O(log              method with constant time approximation
n) on the approximation factor.                            algorithm performs well within its worst
                                                           case performance bounds, and outperforms
    While this gap between constant time
                                                           the naive heuristic by a substantial margin.
approximation algorithm and the optimal
solution is not small, its expected computing
the optimal solution (even if it has to be
done only once) is practically infeasible for              References
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        In this paper an overview of                           Wireless Communications, vol. 13, no.
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networks. This work introduces a number of
                                                               Case for Technology for Developing

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    Regions. IEEE Computer, 38(6):25–38,              AUTHOR BIOGRAPHIES
    June 2005.                                        Mrs. V. Anuradha graduated with B.Sc
[6] P. Dutta, S. Jaiswal, K. Naidu, D.                Computer Science in the year 1995 and
    Panigrahi, R. Rastogi, and A. Todimala.           completed M.C.A at Madras University in
    Villagenet: A low-cost, 802.11-based              the Year 2000. Completed her M.Phil in the
    mesh network for rural regions. In                year 2003 and also got Guide Approval for
    WIreless Systems: Advanced Research               M.Phil in Bharathiar University, Peiyar
    and        Development        Workshop            University, Bharathiar University and
    (WISARD), 2007.                                   currently doing her Ph.d.Hear area of
[7] R. Patra, S. Nedevschi, S. Surana, A.             interest is Networks and data mining. Mrs.
    Sheth, L. Subramanian, and E. Brewer.             V. Anuratha have guided 20 M.Phil scholors
    WiLDNet: Design and Implementation                and she have participated and presented
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    distance networks. In NSDI, 2007.                 international conferences and etc..
[8] B. Raman and K. Chebrolu. Design and
    evaluation of a new MAC for long                   Currently she is working as a H.O.D – PG
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    Mobicom, 2005.                                    Saraswathi Thyagaraja      College with a
[9] D. S. Lun, N. Ratnakar, M. Medard, R.             decade a teaching experience
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                                                       Dr. P. Sivaprakasam :
    Transaction on Information Theory, vol.
    52, no. 6, pp. 2608–2623, June 2006.              He have completed his M.Sc(c.s) in the year
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[11] ilogcplex.                                       papers at national level and 3 at international
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    Algorithms, 19(1), 1995.

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