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A Lightweight Skeleton Construction Algorithm for

Self-Organizing Sensor Networks

Hady S. AbdelSalam

Computer Science DepartmentOld Dominion University,

Norfolk, VA 23529

[email protected]

Stephan Olariu

Computer Science DepartmentOld Dominion University,

Norfolk, VA 23529

[email protected]

AbstractAlthough, current technology enables an inexpensivemassive production of sensors, it raises numerous challenges onthe protocols needed to interact with these sensors efficiently.Several techniques have been proposed to address each ofthese challenges individually (i.e. localization, clustering, routing,aggregation . . . etc). Instead of solving each of these problems in-

dividually facing the same common challenges with each problem,we propose to construct what we call a network skeleton that isconstructed immediately after network deployment and providesa topology that makes the network more tractable. The skeletonprovides sensors with coarse localization information that enablesthem to associate their sensory data with the geographic locationin which the data was measured. Moreover, it promotes ageographic routing scheme that simplifies data communicationacross the network through skeleton sensors. By hypotheticallytiling the deployment area using identical hexagons, the con-struction algorithm clusters sensors based on their locations intohexagons. Skeleton sensors are chosen to be the closest sensorsto the centers of these hexagons. Simulation results show thatthe accuracy of the proposed protocol to establish the skeletonis sufficient to make the approach applicable for most WSNapplications.

I. INTRODUCTION AND RELATED WOR K

Sensors are tiny low-cost devices with usually limited sens-

ing, computational and communicational capabilities. Through

these capabilities, sensors can be networked together to form

what is referred to as a Wireless Sensor Network(WSN).

WSNs have a wide variety of military as well as civilian appli-

cations which include battlefield surveillance, environment and

habitat monitoring, healthcare applications, home automation,

traffic control and others [7], [6], [5].

Sensors are usually deployed in large numbers and in

random fashion. After deployment, we rarely end up with anetwork that is easily managed especially when sensors do

not know their locations, do not know how to aggregate their

sensory data or where and how to route the aggregated data.

The limited energy budget available to sensors makes things

much worse. To save their energy, sensors have to sleep and

wake up asynchronously. Such actions continuously change

0This work was supported in part by NSF grant CNS-0721563 i.e. Col-laborative Research-NeTS-NOSS: AutoNomouS netWorked sEnsoR systems(ANSWER).

the network topology and make the basic network protocols

more difficult.

Different techniques [8],[3], have been proposed to make the

sensor network more tractable by partially solving one of the

inherent network problems (e.g. localization, data aggregation,

routing, clustering . . . etc). Self organizing techniques havealso been proposed to help the network adapt to changes in

topology due to sensor energy depletion or deployment of new

sensor batches [4],[1],[2].

Our approach is a little bit different. We propose to construct

an infrastructure or a skeleton for the network immediately

after deployment. The network skeleton is a group of sensors

that are chosen in a way to satisfy two conditions:

1) They are well distributed across the whole network so

that any sensor in the network is within the transmission

range of at least one of the skeleton sensors.

2) By hopping through skeleton sensors only, there is at

least one communication path between any two skeleton

sensors.

Having such a skeleton can simplify network management

in many different ways. We can summarize some of these

advantages in the following: (1) It provides sensors with coarse

localization information that enables them to associate their

sensory data with the approximate geographic location in

which the data were taken. Many WSN applications(e.g. Bor-

der Protection and Bush Firefighting) doesnt require accurate

location information, as even a few meters localization error

is still acceptable. Moreover, current localization techniques

still have their deficiencies and there is no such technique

that can provide accurate localization all the time for different

environments. Hence, the existence of a network skeletoncan eliminate the need to use any of the current localization

techniques for such applications. (2) Skeleton sensors provide

a complete set of communication paths that can be used by any

geographic routing technique to simplify data communication

across the network. (3) The network can be easily clustered by

taking skeleton sensors as cluster heads and letting sensors join

the cluster of its nearest skeleton sensor. Moreover, a skeleton

sensor can control sleep and wake up cycles for sensors in its

neighborhood saving their energy and prolonging the network

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings

978-1-4244-3435-0/09/$25.00 2009 IEEE

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lifetime.

The remainder of the paper is organized as follows: In

section II, we briefly describe our assumptions for the un-

derlying network model. The details of the proposed skeleton

construction protocol is presented in section III. In section

IV, we show by examples how network skeleton can simplify

many of network management tasks. Simulation results are

summarized in section V. Section VI concludes the paper.

I I . NETWORK MODEL

In our network model, we assume the following:

(1) A sensor node refers to a tiny electronic device with

limited sensing, computational and communicational capabil-

ities. (2) A sensor is powered by a non-renewable on-board

energy source. When this energy supply is exhausted, a sensor

becomes in-operational; hence sensors sleep and wake up

alternatively to save their energy. Sleep and wake up cycles

for different sensors occur asynchronously. (3) Due to massive

deployment, sensors should work unattended as it is either

impractical or infeasible to develop protocols that interact with

sensors individually. In other words, sensors should be treatedas if they were anonymous with no fabrication-time identities.

(4) The network should have an Aggregation Node(AN) or

sink node that is responsible for tasking sensors and getting

the aggregated results back. The AN has no energy constraints

hence it can remain awake all the time. (5) The AN is equipped

with two powerful transceivers with adjustable transmission

range R, one of the two transceivers is unidirectional whilethe other is omnidirectional. (6) Sensors have a maximum

transmission range, tx , assumed to be much smaller thanR. (7) The reception circuitry in sensors should be able todetermine the received signal strength(RSS).

III. SKELETON CONSTRUCTION PROTOCOL

In general, there are different ways we can use to choose

skeleton sensors while satisfying the two conditions mentioned

in section I. However, it is always recommended to distribute

communication load among sensors in order to prolong their

lifetime. Hence, our goal is to choose skeleton sensors in

a way that maximizes the number of communication paths

between any pair of them. The main idea of our protocol is

to divide the deployment area into identical disjoint regions

each of which has exactly one skeleton sensor that is chosen

to be the closest sensor to the center of the region. Region

size is determined such that transmissions of the skeleton

sensor in any region can be received by other skeleton sensors

in all immediate neighboring regions. Since communicationis omnidirectional, using circular regions seems to be the

most appropriate choice. However, circles can not be used

to perfectly tile the deployment area, so we decided to use

hexagons for the tiling purpose as shown in figure 1.

Given, tx, the maximum transmission range of a sensor,we can determine the size of the hexagons (regions) that

perfectly tile the deployment area by the radius of the circle

that passes through the hexagon vertices (i.e. tx3

). The first

hexagon is hypothetically placed so its center coincides with

Fig. 1. Dividing Deployment Area into Sectors

the sink node. Other hexagons, are placed side by side in the

following six directions (i.e. 6, 36, 56, 76, 96

, and 116

). The

geometry of the gaps between the hexagons in any two con-secutive directions allows perfect coverage using sequentially

increasing number of hexagons. We use a ternary coordinate

system sector,row,column to uniquely identify hexagons andskeleton sensors. The deployment area is divided into six

sectors. In each sector, hexagons are stacked in rows. In the

first row, there is only one hexagon(column), in the second

row, there are two, in the third there are three . . . and so on.

The hexagon in column c in row r in sector s is uniquelyidentified using the ternary tuple s,r,c. Sectors and columnsare numbered as shown in figure 1.

Selection of skeleton sensors starts when the sink node

selects the six skeleton sensors in the first row. After that, the

process continues recursively where sensors in any row select

sensors in the next row. This continues until we reach the

boundaries of the deployment area where no more skeleton

sensors can be added. When a skeleton sensor Ss,r,c isselected, there must be rules based on which Sdetermines theskeleton sensors it has to select. To avoid redundancy, reduce

collisions and save sensor energy, we propose the following

selection rules:

1) Only sensors with odd column coordinate are allowed

to select such that sensor Ss,r,2c1 selects sensorsSs,r+1,2c1 and Ss,r+1,2c.

2) There is only one exception relating the first column

in all even rows. Sensor Ss,2r,1 should select sensorsSs,2r+1,1, Ss,2r+1,2 and Ss1,2r+1,2r+1.

3) Selection of a single skeleton sensor takes at most one

time epoch. Selection of skeleton sensors in different

odd sectors (i.e. s = 1, 3, 5) but with the same row andcolumn coordinates occur in the same time epoch. A

similar rule applies for even sectors (i.e. s = 2, 4, 6).

From the above rules we emphasize on the following. Skeleton

sensors with even column coordinate do not select other back-

bone sensors. Selection in odd rows in a single sector requires


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2 time epochs, however selection in even rows requires 3 timeepochs. The total number of time epochs needed to search

in all the six sectors is 4 time epochs for odd rows and 6time epochs for even rows. Figure 1 shows search directions

in sector 5 for the third and the fourth rows.As we mentioned earlier, skeleton sensors are chosen to

be the closest sensors to the centers of their hexagons. The

mathematical formula which a sensor uses to estimate the

distance between itself and the center of a given hexagon

depends on the position of the hexagon center and the angle

of the line that connects the sensor to the sink node. Hence,

it is appropriate to start by showing how sensors can estimate

these values.

Arranging hexagons as described above, sensors can ge-

ometrically calculate, (x, y), the position of the center ofhexagon s,r,c as follows, (see figure 2)

x = xs + r tx cos() + (c 1) tx cos()

= xs + r tx cos

(s 1

2)

3

+

(c 1) tx cos(s +

3

2 )3

(1)

y = ys + r tx sin() + (c 1) tx sin()

= ys + r tx sin

(s 1

2)

3

+

(c 1) tx sin

(s + 3

2)

3

(2)

Where (xs, ys) is the position of the sink node.

Fig. 2. Evaluation of the Position of the Center of a Hexagon

A. Measuring Angles Practically

As mentioned in the network model, we assume that the

sink node is capable of transmitting directionally and omni-

directionally. The directional antenna at the sink node hasa narrow beam-width and can be rotated in any direction.

Transmission physics states that the transmission pattern of

directional antenna consists of a major lobe which is oriented

in the direction of the transmission and several minor back and

side lobes. The received transmission power is maximum at the

center of the major lobe and reduces as we go far from it. For

the purpose of this paper, we simplify the antenna transmission

pattern by representing it as a narrow sector of angle that isdivided in half by the transmission direction beam.

Initially, the sink node uses its omnidirectional antenna to

send a sequence of WAKEUP messages to wake up sleeping

sensors so they can learn their angle to the sink node. Ob-

viously, the number of WAKEUP messages should be large

enough so that the time needed to send these messages is

longer than the maximum sleeping time of a sensor. This

guarantees that all sensors receive at least one copy of the

message. In addition to waking up sensors, the last WAKEUP

message should also provide a level of synchronization among

sensors. The reader might argue that this kind of synchroniza-

tion can not be accurate due to the different transmission,

propagation and processing delays suffered at each node.

Despite this inaccuracy (in the order of microseconds or even

a few milliseconds), the achieved level of synchronization is

enough for our purpose especially in the existence of the

mechanical delay of rotating the directional antenna.

Immediately, after sending the last WAKEUP message, the

sink node uses its directional antenna to send angle estimation

messages starting from an initial angle 0. After sendinga message, the sink node rotates its antenna either in the

clockwise or in the anti-clockwise direction for a small angle, then it sends the next message. Each angle estimationmessage should contain the current angle of transmission and the initial transmission power p0. When a sensor receivesa recognizable angle determination message, it stores the angle

along with the inverse of the difference in power betweenthe initial transmission power and the received power 1

p0pr .When the antenna of the sink node returns back to the initial

angle 0, it either stops or start a new another cycle usingdifferent values for the transmission power p0 and the rotationangle . Obviously, there is a trade off between the accuracyof the estimated angles and the number of cycles needed which

will definitely affect the time and energy consumption.

After the last angle estimation cycle terminates, a sensor

can estimates its angle to the sink node as the average of

the received angles weighted by the inverse of the difference

between the initial transmission power and the received power

(i.e. 1p0pr ). Mathematically, this can be written as,

=

ni=1

ip0prin

i=11

p0pri(3)

In equation(3), received angles are weighted using 1p0pr

to reduce the impact of multipath, shadowing, and signal

reflections on the accuracy of the estimated angle. Recall thatthe received power of a signal decays proportionally with the

inverse of the traveled distance raised to some power (path loss

exponent). Reflected signals travel a distance that is longer

than the distance traveled by direct signals. Hence, although

the transmission power p0 is the same (for the same cycle), thereceived power of reflected signals should be smaller than the

received power of direct signals. This way weighting angles

based on the received power should reduce the impact of

reflected signals on the accuracy of the estimated angles.


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B. Selection of Skeleton Sensors

In this subsection, we show how a sensor is chosen to be

the skeleton sensor representing the hexagon identified by the

tuple s,r,c. Initially, the searching entity S(it could be thesink node or another skeleton sensor) computes , the anglebetween the sink node and the center of the hexagon identified

by the given tuple using,

= 3

s 1

2+ c 1

r

(4)

After that, S broadcasts a message to all the sensors inthe neighborhood around it asking for sensors with angle

with the sink node to declare themselves. Sensors thatreceive this message for the first time check if the absolute

difference between their measured angle i and is withinacceptable range (i.e. |i | threshod). Each sensorwithin the range estimates ei, the distance between itselfand the hexagon center and initialize an internal countdown

timer to this value. Calculation of ei is presented in detailsin subsection III-C. When the timer of any of these sensors

expires, the sensor realizes it is the closest sensor to the center

of the hexagon identified by the tuple s,r,c. The sensorbroadcasts a message to all his neighbors announcing itself

as the skeleton sensor of the hexagon. Sensors that receive

this message stop their timers and use this message among

other messages they receive from other skeleton sensors to

determine their hexagon. Although collisions are unlikely to

happen, we are still able to break ties by allowing colliding

sensors to compete in another countdown round starting from

a randomly selecting value.

C. Estimation of Selection Error

We show how a sensor can estimate ei, the distance betweenitself and the center of the target hexagon identified by the

tuple s,r,c. We distinguish between two different cases.

Fig. 3. Estimation of Selection Error

Case I: this case is applicable only for the six skeleton sensors

in the first row of each sector. Figure 3(a) shows ei whensensor S is selected to represent the hexagon si, 1, 1. Fromthe figure, ei can be evaluated as,

ei =

tx2 + d2 2 tx d cos(i i) (5)

Where d is the distance between the sink and the sensor andis estimated using RSSI.

Case II: this case is applicable for all skeleton sensors other

than those handled by Case I. As shown in figure 3(b), we

assume the existence of another skeleton sensor S0 that hadbeen previously selected by the protocol to represent the

hexagon Ss0,r0,c0. The selection error of sensor S0 is e0and represents the distance between S0 and the center of thehexagon Ss0,r0,c0. Based on the selection rules we describedearlier, it is S0 turn to select sensor S1 to represent the hexagonSs1,r1,c1. S1 is selected such that the selection error e1 isminimum (e1 is the distance between S1 and the center of thehexagon Ss1,r1,c1). Now, our goal is to provide an expressionfor e1 that can be evaluated by each sensor independently.

As we mentioned in subsection III-B, the searching sensor

S0 must send a message to sensors in its neighborhoodasking the closest sensor to the target hexagon center to

announce itself to other sensors. To avoid repeating the same

calculations at each sensor, sensor S0 should evaluate allcommon terms and sends them within the message it sends

to its neighboring sensors. These terms include the following:(1) Z0 =

X20 + Y

20 , the Euclidean distance between the

sink node and node S0. (2) 0, the measured angle betweenthe line connecting the sensor S0 to the sink node and thepositive x axis. (3) In addition to Z0 and 0, S0 also evaluatesand sends W1 and 1. W1 is the distance between the centerof the target hexagon s1, r1, c1 and the sink node. 1 isthe angle surrounded by the line connecting the sink node to

the center of the hexagon Ss1,r1,c1 and the positive x axis.Mathematically, W1 and 1 can be evaluated using,

W1 =X21 + Y

21

1 =

3s1

1

2 +

c1 1

r1

Where (X1, Y1) is the position of the center of the hexagonSs1,r1,c1. X1 and Y1 are evaluated using equations 1 and 2.

When a sensor receives the message containing Z0, 0,W1and 1, it uses RSSI to estimate r, the distance between itselfand sensor S0. Using the trigonometric law of sines, eachsensor calculates Z1, the distance between itself and the sinknode as follows,

r

sin(1 0)=

Z0sin( 1 + 0 )

= 1 + 0 sin1Z0 sin(1 0)

r

Z1 =r2 + Z20 2 r Z0 cos() (6)

Finally, each sensor can apply the trigonometric law of cosines

to evaluate e1 as,

e1 =W21 + Z

21 2 W1 Z1 cos(1 1) (7)

It is also worthwhile to mention that sensors which evaluate

e1 to be larger than some threshold value emax should notinitialize their internal timers. This decision implicitly provides


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the stopping criterion upon which the boundaries of the

deployment area are determined.

IV. SKELETON BASED NETWORK MANAGEMENT

Recall that the main goal behind constructing a skeleton

is to provide an infrastructure that makes the network more

manageable. In this section, we briefly show how the basic

network management tasks can be simplified using our pro-

posed skeleton.

Coarse Localization: The locations of backbone sensorsare estimated during skeleton construction. After being

localized, backbone sensors can be treated as beacons and

the locations of non-backbone can be estimated using the

weighed centroid approach.

Geographic Routing: Given the coordinates of the sourceand the destination in the ternary system, we can easily

find a path from the source hexagon to the destination

hexagon by hopping through sensors inside the hexagons

in between.

Data Aggregation: Non-backbone sensors within any

hexagon can report their sensory data to the backbonesensor in their hexagon which aggregates the data before

sending it the sink node.

Clustering and Leader Election: The skeleton construc-tion algorithm implicitly clusters network sensors based

on their locations. Each hexagon represents a cluster.

The backbone sensor around the center of each hexagon

is the cluster head which can be always elected as the

leader when necessary to coordinate between sensors in

its hexagon for any centralized protocol.

V. SIMULATION RESULTS

We built a simulator of a WSN that implements the proposed

protocol to construct a skeleton for the network. We run oursimulator assuming different network densities ranging from

0.01 up to 0.20 sensors/m2. Sensor maximum transmissionrange was set to 15m. We assumed a square deployment area(200X200m) that has a single sink node that is placed in itscenter (0, 0). Sensors were distributed randomly across thedeployment area. Errors in RSSI-based angle and distance

measurements were assumed to normally distributed N(0, 1).Figure 4 shows a plot of the skeleton sensors chosen by the

proposed protocol and compares the actual and the estimated

positions of the chosen sensors. Figure 5 shows a plot of the

actual hexagons constructed out of the simulation. Although

the regions do not look like hexagons, they are positioned

correctly and it is easy to determine their boundaries.

VI . CONCLUSIONS

In this work we proposed a simple scheme to construct a

skeleton for WSN immediately after network deployment. Our

technique relies on the existence of a single sink node that is

capable of transmitting directional and omnidirectional. We

also built a simulator of the proposed construction protocol.

Simulation results showed that the proposed protocol can

construct a strongly connected skeleton that is well distributed

ActualPositions Estimated Positions

-100

100

100

-100

Fig. 4. Actual vs Estimated Positions of Skeleton Sensors.

Fig. 5. Hexagons Constructed by Simulation

across the whole network. The constructed skeleton can sim-

plify network management in many different ways. It provides

coarse localization mechanism that enables sensors to local-

ize themselves. Moreover, the protocol provides a clustering

mechanism by which sensory data can be easily aggregated

to the sink through skeleton sensors. In addition to this, the

ternary coordinate system defined by the hexagons provides

an implicit kind of map for geographic based routing.

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[3] S. Lederer, Y. Wang, and J. Gao. Connectivity-based localization of largescale sensor networks with complex shape. INFOCOM 2008. The 27thConference on Computer Communications. IEEE, pages 789797, April2008.

[4] D. C. Marinescu, G. M. Marinescu, and C. Yu. Self-organizing sensornetworks. Wireless Pervasive Computing, 2008. ISWPC 2008. 3rd

International Symposium on, pages 288292, May 2008.[5] S. Olariu, M. Eltoweissy, and M. Younis. ANSWER: AutoNomouS net-

Worked sEnsoR system. Journal of Parallel and Distributed Computing,67(1):111124, 2007.

[6] P. Saffo. Sensors, the next wave of innovation. Communications of theACM, 40(2):9397, 1997.

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