www.elsevier.com/locate/comcom

Computer Communications 29 (2006) 2261–2268

A topology discovery algorithm for sensor network usingsmart antennas

Ahmed M. Khedr *, Walid Osamy

Mathematical Department, Faculty of Science, Zagazig University, Zagazig, Egypt

Received 29 May 2005; received in revised form 20 February 2006; accepted 1 March 2006Available online 29 March 2006

Abstract

Wireless sensor networks have recently attracted lots of research effort due to its wide range of applications. In this paper, we focus onsensor network topology discovery problem, where accurate network topology information is important for both network managementand application performance prediction. We present on demand algorithm to discover the sensor network topology. The node thatreceives our topology request collects all topology related information from each node in the network and constructs link informationdatabases.� 2006 Elsevier B.V. All rights reserved.

Keywords: Smart antenna; Sensor network; Topology discovery; Forwarding database

1. Introduction

A sensor network consists of a collection of sensors dis-tributed over some area that form Ad Hoc network. Eachsensor node is equipped with some limited memory andprocessing capabilities, multiple sensing modalities andcommunication capabilities. The topology information ofthe sensor network is an important aspect for the supervi-sor, for example, the network supervisor of a sensor net-work will need the topology information to know theareas that are not monitored by the sensor nodes, the nodesthat run out batteries and the nodes that carried out awayby wind or get eaten by wild boar. These changes are dis-covered by topology discovery algorithms. Topology dis-covery algorithms will help in maintaining connectivityand conserving the rare resources, such as power and band-width of the network.

An omnidirectional antenna is an antenna that trans-mits and receives equally in all directions. The naturalbroadcasting characteristic of an omnidirectional antenna

0140-3664/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.comcom.2006.03.002

* Corresponding author. Tel.: +20 102093552; fax: +20 055 2308213.E-mail address: amkhedr@yahoo.com (A.M. Khedr).

limits both the medium use efficiency and the bandwidthreutilization efficiency. For these reasons, directionalantennas were designed to fix the radio propagation direc-tions. However, directional antennas do not eliminate themost significant disadvantage of omnidirectional antennas,i.e., interferences. The next step in designing antennastherefore has to be the deployment of antennas that canminimize these interferences. These antennas are calledsmart antennas. A smart antenna is an antenna composedof many antenna elements that are arranged in a linear, cir-cular or planar configuration. The number of these antennaelements is a characteristic of the smart antenna. Their roleis to increase the radio signal quality by optimizing radiopropagation and to increase medium capacity by increasingbandwidth reutilization. Their smartness resides in thecombination of the signals received within the smart anten-na elements. This combination is ensured by the DigitalSignal Processing (DSP). So we consider the use of smartantenna systems in order to achieve reliable and efficientdata delivery in wireless sensor networks.

In this paper a topology database called FDB is con-structed by collecting topology link information from allnodes where link information is defined and identified by

2262 A.M. Khedr, W. Osamy / Computer Communications 29 (2006) 2261–2268

the IDs of two nodes that it connects. This topology data-base is able to answer queries, for example, the query of theexistence of a path to a certain destination.

The rest of this paper is organized as follows. Section 2;describe the previous studies on the topology discoveryproblem. The description of relevant terms are introducedin Section 3. In Section 4, we introduce the algorithm tocarry out topology discovery based on smart antennas.The simulation of our algorithm is presented in Section5. In Section 6, we compute the complexity of our algo-rithm. In Section 7, we conclude this work.

2. Related research

The growths in hardware and wireless network technol-ogies have created low cost, low power, multi functionalminiature sensor devices. These devices make up hundredsor thousands of Ad Hoc tiny sensor nodes spread across ageographical area. These sensor nodes collaborate amongthemselves to establish a sensor network. Sensor networkspromise to revolutionize sensing in a wide range of applica-tion domains. Examples of such applications include: finegrain monitoring of habitats with a view to understandingecosystem dynamics [5]; military and civilian surveillance[10,13,18]; data gathering in instrumented learning envi-ronments for children [27]. The variety of these applica-tions clearly conveys the enormous potential impact ofwireless sensor networks.

Each sensor node has wireless communication capabilityand sufficient intelligence for signal processing and for dis-seminating the data. The limited energy, computationalpower and communication resources of a sensor noderequire the use of a huge number of sensor nodes in a widerregion. This large number also allows the sensor networkto report with greater accuracy of information. Sometimesthere is no enough sensors to deploy to reach the desirednode density, this problem of low network density over-come by deploying dummy nodes along with the sensornodes. A dummy node is a low-cost node, whose only func-tionality is to broadcast its group identity to its neighbors.A dummy node does not need to find its own location, nordoes it need to carry out sensing or computing tasks [11].Here in our work, we don’t consider dummy sensor nodes,we consider that each node can carry out sensing or com-puting tasks. Communication in sensor networks is nottypically end to end. Energy is typically more limited insensor networks than in other wireless networks becauseof the nature of the sensing devices and the difficulty inrecharging their batteries.

Network topology is an important model of the networkstate as it implicitly gives a lot of information about theactive nodes present and the connectively map of the net-work. Since the success of the topology discovery algo-rithm depends on the reliability of broadcasts [24]. In oursetting, to discover the topology information we need abroadcasting schema that taking into account the smallcommunication throughput and the limited memory and

computational capabilities of sensor networks. Broadcast-ing in wireless sensor networks is a very common opera-tion. The easiest and most straightforward way to dobroadcasting is by flooding. However [21] studies thebroadcast storm problems and shows that flooding is verycostly in terms of energy and can result in serious redun-dancy, contention and collision. It also proposes severalschemes to alleviate this problem.

In our work we handle broadcasting problem by usingsmart antennas. Sensor nodes can be integrated with smartantenna systems to significantly decrease the nodes’ powerconsumption, and therefore increase their life cycle and toachieve reliable and efficient data delivery in wireless sensornetworks. Tassos et al. [7] pointed out the feasibility andnecessity of using smart antennas in sensor networks, aswell as the advantages that are presented to communica-tion links due to their use. Also Hend [16] showed that bat-tery power utilizations and bandwidth use can be improvedby using smart antennas. Therefore, the use of smart anten-nas in senor nodes is feasible, and highly desirable.

Many topology discovery algorithms exist for wired net-works but most of them introduce a lot of additional trafficinto the network [8,26]. Since sensor networks are energyconstrained [10,28], the protocols used in sensor networkshave to be energy efficient [12,14]. There has been somework related to topology discovery for sensor networks,in [20] an algorithm for self configuring sensor networksbased on flooding and gossiping methods with some newparameters to discover the topology for home sensor net-works is given. Deb et al. [6] presented hierarchical treebased clustering scheme gathers neighborhood informationfrom all sensor nodes which provide only partial link infor-mation. In RoyChoudhury et al. [23] used the mobileagents to discover the network topology where the mobileagents in the nodes periodically gather topology informa-tion and disseminate it to all the other nodes in the net-work. In Adnan et al. [1] proposed a mobile multi agentsystem for topology discovery that would allow fault man-agement functions in Ad Hoc network. They hold a com-parison to some of the existing mobile agent basedsystem and shows that using agents in the nodes lays downthe framework for fault management and efficient nodemonitoring. Zhou et al. [30] presented four localized topol-ogy generation mechanisms and shows how localized selfconfiguration mechanisms can impact the global networkbehavior.

In [3], Ranveer et al. showed that the broadcasts in mostMACs for Ad Hoc network are not reliable and they havepresented a variation on the MAC protocol to overcomethe problem of collision and to ensure that the broadcastreaches at one node in the neighborhood, they used themodified MAC to discover the network topology whichgave a good performance in the discovery algorithm. Inour work, we assume that each node equipped with smartantennas for both transmitter and receiver which leads tomore reliability of broadcasts, where smart antennas havethe capability to save nodes in the network from receiving

A.M. Khedr, W. Osamy / Computer Communications 29 (2006) 2261–2268 2263

the same broadcast packet many times over while keepingthe same reachability as omnidirectional antenna, more-over smart antennas ensure a better utilization of the powerbattery and radio medium [16]. In [4], they used a clusteringschema to discover the network topology. The clusterheads are dynamically chosen based on geographic loca-tion or network connectivity and the MIBs at cluster headsare used to gather topology information. Our work is sim-ilar to [4] in the concept of cluster heads where in our work,nodes at lower level are considered as cluster heads for thenodes at the higher level and the topology information iscollected in topology database called FDB.

Routing is of central importance in Ad Hoc networks.Since wireless sensor networks similar to mobile Ad Hocnetworks so closely, several protocols for Ad Hoc havealready been proposed for deployment such as DSDV,DSR, and AODV [2,9,22]. These protocols are suitablefor Ad Hoc network but we can not apply them directlyfor sensor network. In case of sensor networks, the nodeshave very limited energy and there is no external sourceof battery input power. The routing techniques in sensornetworks are classified based on the network structure intothree categories: fat, hierarchical, and location based rout-ing protocols. Furthermore, these protocols are classifiedinto multipath-based, query-based, negotiation-based, orQoS-based routing techniques depending on the protocoloperation examples of these routing protocols in[12,15,17]. In [7] the authors showed that the improvementsin the performance of the sensor network and how routingin sensor networks can be accomplished with minimal com-putations and power consumption when the proposed useof smart antennas is imposed.

3. Description of relevant terms

We assume that we work with sensor nodes that are ran-domly distributed and they are having no knowledge abouttheir neighbor nodes. Also we consider that each node isdistinguishable by unique identifier such as MAC address,and each is equipped with smart antenna. Our goal is todesign an algorithm that determines the topology of thenetwork. To accomplish this goal, we choose to drive thenetwork topology by directing topology request messageto any sensor node in the network, and then obtain thetopology information from the node which received ourrequest message. In the following subsections we introducea description of some relevant terms like smart antenna,forwarding databases, and complete forwarding databases.

3.1. Smart antenna

Smart antenna is one of the most promising technolo-gies that enables a higher capacity in wireless networksby effectively reducing multi-path and co-channel interfer-ence [19,29]. This is achieved by focusing the radiation onlyin the desired direction and adjusting itself to changingtraffic conditions or signal environments. A smart antenna

system employs a set of antenna elements with signal pro-cessing capability to optimize its radiation and/or receptionpattern automatically in response to the signal environ-ment. There are two kinds of smart antennas, switchedbeam antennas and adaptive array antennas.

3.1.1. Switched beam antennas

A switched beam antennas form multiple fixed beamswith heightened sensitivity in particular directions. Theseantenna systems detect signal strength, choose from oneof the several predetermined, fixed beams, and switch fromone beam to anther for transmission or reception.

3.1.2. Adaptive array antennasIn an adaptive array antenna, the adaptive algorithm

assigns complex weights to each element. These weights areiteratively updated. The assigned weights decide the result-ing beam pattern of the antenna array. The individual beampattern of the elements can be omnidirectional or direction-al. When individual gain pattern are combined with complexweights, the combined antenna beam pattern points towardsthe desired direction, i.e., the antenna array has its maximumgain towards the desired angle of the arrival.

The difference between switched beam antennas andadaptive array antennas, the switched beam antennas focustheir smartness on detecting the higher radio signal levelwhereas the adaptive array antennas benefit from all theinformation received within all the smart antenna elementsand use it to optimize the signal output via a weighting sys-tem that adjusts the reception level within each smartantenna element.

We consider that both the transmitter and the receiver ofeach sensor node will use smart antenna techniques, and thesmart antennas are implemented using adaptive array algo-rithm. The advantage of this approach is the improvementin the channel access efficiency of the network [25].

There are some issues that arise for topology discoveryproblem. These issues can be summarized by the followingquestions: How does node discover its neighbors? How isthe problem of broadcast handled? What is if we need toknow the history of topology changes?

After the deployment each sensor node that equippedwith smart antenna needs to update its transmitting andreceiving beam pattern by adjusting its weight vector look-up table also the initial phase in topology discovery is thateach sensor node needs to discover its round neighborsfrom that point we can run the topology discovery algo-rithm immediately after deployment to begins discoveringprocess and to let the adaptive beamforming algorithmsupdate its patterns as follows. In discover phase, each nodeis in one of the two nodes, searching or listening node.When searching it starts with an omnidirectional beampat-tern and as the node starts to communicate with othernodes the algorithm builds up a weight vector lookup tableto use for transmit beamforming. When a node receives apacket, its adaptive receive beamforming algorithm willupdate the received weight vector. This weight vector will

E

A

R

B

C D

F

t1

t6

t3t4

t2

t5

J

Kt8

t7

t12t9

t10

t11

Fig. 1. The sensor network state after period of time.

Table 2FDB complete for node R

ID DCN TOAM Level Location

R 0 x1, y1

A R t1 1 x2, y2

B R t2 1 x3, y3

C R t3 1 x4, y4

D R t4 1 x5, y5

E C t5 2 x6, y6

F C t6 2 x7, y7

J B t7 2 x8, y8

K D t8 2 x9, y9

F E t9 2 x10, y10

E A t10 2 x11, y11

B A t11 1 x12, y12

C D t12 1 x13, y13

2264 A.M. Khedr, W. Osamy / Computer Communications 29 (2006) 2261–2268

result in a beampattern that is pointing towards the desiredtransmitter. The same weight vector can be used by trans-mitter to point the transmit beampattern towards thedesired node. As the network communication proceedsevery node will start to update its transmit weight. Gradu-ally all the communication will be directed via transmitbeampattern and adaptive receive beampattern. When lis-tening, it receives packet, the node will store the convergedweight vector to transmit look up table for transmitter. Thetransmitter will use this stored weight vector to transmitthe packet. The receiving algorithm will continue to updatethe look up table every time it receives a packet. By thisway the two tasks performed at a time discovering neigh-bors and updating the beampatterns.

In a few words, our algorithm makes each sensor nodediscover its neighbor nodes by sending AD message inomnidirectional mode, this let the smart antenna algorithmin each node to update its weight look up table and formthe desired weights at each node. Where the smart antennaalgorithm uses the received signal to converge and formbeam towards the desired transmitter. The weight vector isthen stored in a weight look up table to be used by the trans-mitter. When the node wants to reply to a sender, it looks upthe desired weight from the weight vector table and formstransmits beam pointing towards the desired node.

3.2. Forwarding database FDB

The forwarding database (FDB) is the database thatmaintains the reachability information for each node inthe network. The FDB structure takes the table form withthe attributes ID, DCN, TOAM, Level, Location, whereID is the node identification number, the (DCN) is IDsof direct connected nodes, TOAM is the time of arrivalmessage from sensor node to sensor node, level, and loca-

tion is the node level and location.After the deployment of the sensor nodes, each node

forms its Forwarding database which only contains currentnode information. For example, Table 1 represents theformed FDB of node R which belongs to the sensor net-work shown in Fig. 1. The entry of FDB is updated withevery discovered new node.

3.3. Complete FDB

The FDB for a sensor node is said to be complete if itcontains all the forward entry for each neighbor node athigher level. If the node is a border node (node at highestlevel) then its FDB is complete. The complete FDB con-tains all possible links between any two nodes in thenetwork.

Table 1The FDB entry for node R

ID DCN TOAM Level Location

R 0 x,y

In Fig. 1 node R has nodes A, B, C, and D at level oneand E, F, J, and K at level two. Table 2 shows the completeFDB of node R, where its FDB contains all topology relat-ed information from each node in the network.

Also in Fig. 1, node C will have a complete FDB, if itcontains the complete FDB of node E and F (i.e., theFDB status of node E and F is complete), where nodeE and F at the higher level of node C. Also nodes Jand K have complete FDB because they are bordernodes.

4. Algorithm outlines

After the deployment of the sensor nodes over the area,all nodes are in the idle state, i.e., they have no knowledgeabout their around neighbors. The FDB of idle node con-tains only its entry, i.e., its ID, Location, assigns its level tozero also it has no DCN and its FDB status is set to beincomplete.

In our work the sensor node becomes active node in thefollowing two cases:

• Case 1: when the node receives topology request mes-sage from the user;

• Case 2: when the node receives message from its parent(direct connect node) contains topology request.

Note: The active node ignores any topology request inany message but it will adds the sending node ID asDCN in its FDB at the same level of the active node. InFig. 1 E will be active after receiving advertising (AD) mes-sage from C. In this case the topology request message

A.M. Khedr, W. Osamy / Computer Communications 29 (2006) 2261–2268 2265

from F to E will be ignored but E will add F in its FDB atthe same level of E.

In our algorithm, the node that receives the user topol-ogy request message, will consider itself as network coordi-nator (zero level), and the level number keeps increasing byone till reach the border nodes, i.e., coordinator node is thecenter of some circles that have different radii, each radiuswill be increased by one from the previous radius till reachthe out side circle.

There are two main phases in our algorithm, the firstone is the Discover Phase and the second one is the Aggre-

gation Phase.

4.1. Discover phase

A sensor node enters the Discover Phase after becomingactive node, to discover its around neighbors by transmit-ting AD message in all directions except the direction ofthe nodes in its DCN list and then waits a period of timeproportional to its transmission power.

We will call the node which receives a topology requestfrom user or parent node a Sender and the node whichreceives the AD message a Recipient.

The following code will be executed at every active node.Procedure Discover()

(1) Whenever a sensor node (Sender) receives a requesttopology from user or parent, it will transmit AD

messages in all directions except the directions ofthe nodes in its DCN list.

(2) While (there is a response to the AD message from aRecipient).

(a) The Recipient will update its smart antenna

system to direct its beam toward the Sender to r-esponse it with ok! message.

(b) The Sender, after receiving the response ok! mes-sage from the Recipient, will update its smart a-ntenna system to direct its beam toward theRecipient to reply it by sending the followinginformation:

• The Sender ID,• The Sender level,• Topology request.

(c) According to the received information from theSender, the Recipient will update its FDB as thefollowing:

• The Recipient DCN will be the parent ID

(Sender ID),• The Recipient level will be the Sender level + 1,• Assign TOAM.

(d) The Recipient the new Sender will transmit AD

messages in all directions except the direction ofthe nodes in its DCN list.

(3) End while(4) The sensor network nodes enter the Aggregation

Phase if there is no any responses to all Senders,i.e., we reached the border level.

4.2. Aggregation phase

The active node that exits from the discover phase andhas neighbors at higher level, is in the aggregation phase tillcomplete its FDB. The active node exits from aggregationphase and returns to the idle state after completing itsFDB.

In aggregation phase the nodes at the higher level com-plete their FDBs and then forward them to the DCNneighbor nodes at the lower level. The lower level nodesupdate their FDBs as follows:

If FDBreceive is the received FDB from higher level node,and FDBi is the FDB of node i in the next level toward thecoordinator node, FDBi will be updated by running the fol-lowing UPDATE query.

Insert into FDBi

select * from FDBreceive where not exists

(select * from FDBi where

(FDBiÆID = FDBreceiveÆID OR FDBiÆID = FDBreceiveÆDCN)AND

(FDBiÆDCN = FDBreceiveÆID OR FDBiÆDCN =FDBreceiveÆDCN))

In the above UPDATE query, we insert only thenew links between any two nodes into the FDBi fromFDBreceive.

The forwarding and updating of the FDB from higherlevels to lower levels will be continued till reach the coordi-nator node. The completed FDB of the coordinator nodewhich constructs the topology of the entire network, willbe directed to the end user.

The following algorithm shows how the aggregationphase occurs at every node and how we get the completeFDB.

Procedure Aggregation(FDBreceive)

(1) Input: The received FDBs (FDBreceive)(2) Output: The complete FDB of the coordinator

node.(3) If (the node is a border node)

(a) Change the node FDB status into complete.(b) Send the complete FDB to its DCN neighbor node.

(4) Else

(a) While (receiving FDBreceive)

• Run the Update query

(b) End while(c) Change the status of the current node FDB to

complete(5) End if(6) If (node DCN neighbor == Null)

• Send the complete FDB to end user

(7) Else

(a) Send the complete FDB to the DCN neighbor node(8) End if(9) End Algorithm

Communication Range

% o

f dis

cove

red

node

s

dense networkspare network

Fig. 2. % Number of discovered nodes vs communication range.

Communication Range

Num

ber

of L

evel

s

Fig. 3. Number of levels vs communication range.

2266 A.M. Khedr, W. Osamy / Computer Communications 29 (2006) 2261–2268

After the end user receives topology database, the net-work topology may be changed after a period of time dueto any exceptions. To act upon these changes, the end usercan send new topology request message to receive newFDB. However for most cases, we don’t need to discoverthe full network topology again, where by a particular nodechanges, that node after receiving update request, broad-casts a topology database update message to adjacent nodesto be forward to the coordinator node and the coordinatornode by its role forward these updates to the end user.

5. The simulation results

In this section we analyze the performance of our pro-posed algorithm. Our topology discovery algorithm is eval-uated by comparing the percentage of discovered nodes inthe network to the actual number of sensor nodes.

We use the same antenna model as discussed in [25]. Inthis model a modified MAC is proposed where an adaptivebeam forming technique is used to steer the beam pattern ofthe antenna array with two or four antenna elements, also amixed approach is used where both the transmitter and thereceiver of a given node is attached with smart antenna.

In our simulation, the environment is assumed to beclosed area of 100 · 100 m2 in which sensor nodes are distrib-uted randomly. The number of sensor nodes and the commu-nication range of the sensors vary according to theexperiment requirements. The results represent an averageof these values for different runs. The first part of thedesigned experiments is to find the effect of node positionon our proposed algorithm. Next, we evaluate the effect ofcommunication range and the number of sensors in the sen-sor network.

Our simulation experiments show that:

• Directing the topology request to sensor node at net-work border increases the number of formed levels,and the delay time of returning the complete FDB morethan directing the topology request to inner sensor nodein the network.

• The trained smart antenna systems at first phase makesthe aggregation phase runs in acceptable manner whichrapidly leads to complete FDB.

• By increasing the communication range of the sensornodes, the number of formed levels decreases and thediscover phase ends fast which makes the second phaseto begins and ends fast.

• If the sensor nodes populated such that each node with-in communication range of other nodes, our topologydiscovery algorithm performs extremely well.

• In case of dense networks our algorithm discovers closeto 100% of sensor nodes, and close to 60% in sparenetworks.

Fig. 2 shows that the percentage of discovered sensornodes increases in dense networks more than in sparenetwork.

Fig. 3 shows that as the communication range increases,more sensor nodes will be discovered and the number offormed levels decreases which makes our algorithm goesfast.

6. Complexity analysis

In this section we present analysis of the networkload. We are mainly considering the energy expendedin communication (transmission and reception of pack-ets) as the network load. This is because it is far greaterthan the energy consumed by the processor in computa-tion. There are two main factors contributing to the net-work load.

• The number of packets exchanged in node vicinity.• The traffic load on the intermediate nodes for routing

the response back to the coordinator.

In our algorithm every node broadcasts in all directionsonly one time to discover who is around and in what direc-tion. Then all the communications in the network occur ina smart manner where every node in the network learnswhere to direct its beam. If we assume that n is the totalnumber of sensors in the network and Nnighs is the averagenumber of around neighbors to any sensor.

In discover phase, each node transmits a message in alldirections except the directions of its DCN list, receivesresponses from its neighbors, and then transmits request

A.M. Khedr, W. Osamy / Computer Communications 29 (2006) 2261–2268 2267

message. Therefore, the number of exchanged packets willbe approximately 3 * Nnighs for each node.

If we assume

• PSad is the packet size for AD,• PSrequest is the packet size for updating and topology

request, and• PSresponse is the packet size of the response packet.

Hence, the traffic generated in the discover phase will be

traffic generated ¼ Nnighs � ðPSad þ PSresponse þ PSrequestÞ.ð1Þ

In aggregation phase, each node knows where to direct itsbeam and the flow of messages begins from outer levels to theinner levels toward the coordinator node. The number ofpacket exchanged in this phase is approximately n � 1. Ifwe assume that the packet size of the FDB is PSFDB, hencethe traffic generated in the aggregation phase will be

traffic generated ¼ ðn� 1Þ � PSFDB. ð2ÞTherefore, the total number of exchanged messages to

report the end user the complete FDB will be

Exchanged Messages ¼ 3 � N nighs � nþ ðn� 1Þ; ð3Þ

and the total traffic generated will be

traffic generated ¼ 3 � Nnighs � nðPSad þ PSrequest

þ PSresponseÞ þ ðn� 1Þ � PSFDB. ð4Þ

7. Conclusion

In this paper, we have described a topology discoveryalgorithm for wireless sensor networks. The algorithm con-sists of two phases, the first phase discovers the aroundnodes and in that phase the smart antenna algorithm builtthe desired beam pattern that made all communicationbetween the sensor nodes occurred in a smart manner.The second phase aggregates the complete link informationof sensor network in a database that can be used for anykind of applications. We worked with sensor nodes thathave smart antennas for both transmitter and receiver,these nodes are randomly distributed and have no knowl-edge about their neighbor nodes. Our algorithm logicallyorganizes the network in the form of clusters, where theinner level nodes are considered as cluster heads for outerlevel nodes. Our simulation results show that the algorithmdiscovers close to 100% of the network links in dense net-works and close to 60% in spare networks.

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Dr. Ahmed M. Khedr received his B.Sc degree inMathematics in June 1989 and the M.Sc degree inthe area of optimal control in July 1995 bothfrom Zagazig University, Egypt. In March 2003he received his Ph.D. degree in computer sciencefrom University of Cincinnati, Ohio, USA. FromMarch 2003 to January 2004, he was a researchAssistant Professor at ECECS Department Uni-versity of Cincinnati, USA. From January 2004till now he is working as Assistant Professor atDepartment of Mathematics, Faculty of Science,

Zagazig University, Egypt. He has coauthored 20 works in journals andconferences relating with optimal control, distributed databases, sensor

network and decomposable algorithms.