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T. Enokido et al. (Eds.): EUC Workshops 2005, LNCS 3823, pp. 1138

© IFIP International Federation for Information Processing 2005

–

1147, 2005.

FERMA: An Efficient Geocasting Protocol for Wireless

Sensor Networks with Multiple Target Regions★

Young-Mi Song, Sung-Hee Lee, and Young-Bae Ko

College of Information and Communication,

Ajou University, Suwon, South Korea

{ymsong, sunghee, youngko}@ajou.ac.kr

Abstract. Some sensor applications are interested in collecting data from

multiple regions. For supporting such applications with multiple target regions,

most conventional protocols are based on either a network flooding or multiple

unicastig to cover those more than one target region. Either one will result in a

lot of redundant packets to transmit by energy scared sensor nodes. To alleviate

this problem, we propose a novel geocasting scheme which can make a suitable

shared path among multiple target regions. We utilize the theorem of “Fermat

Point,” in order to find an optimal junction point branching into each region. By

using this shared path, an interest dissemination can be performed very

efficiently. Our simulation study shows that the proposed scheme FERMA

reduces a lot of network traffic and achieves significant energy saving as the

number of target regions increase.

1 Introduction

Advances in wireless embedded technologies make it possible to enable small and

resource-limited sensor devices to have wireless communication and computational

capabilities [1]. Wireless sensor networks (WSNs) with a large number of such smart

sensors can be deployed for tracking targets or gathering information about physical

phenomena. For many applications in wireless sensor networks [2, 3], a query (also,

called as an interest) is commonly used to have sensor nodes collect data from their

environments and return these sensing data to a query initiator (i.e., the originator of

the interest message). In such query-based sensor networks, an interest message

specifies a particular condition to match events; for example, a type of sensing tasks,

location information where interesting events might occur, an interval between data

propagations, and the lifetime of the query.

There are several approaches for efficiently disseminating interest messages to a

target region. A flooding mechanism, which requires any intermediate receiver to

rebroadcast a non-duplicated interest packet to all its neighbors, is the most

commonly used technique. For example in directed diffusion [3], one of the well-

known query-based routing protocols in wireless sensor networks, a sink node is

★ This work was supported by the Korea Research Foundation Grant funded by the Korean

Government (R05-2003-000-10607-02004) and also supported by the MIC (Ministry of

Information and Communication), Korea, under the ITRC program.

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FERMA: An Efficient Geocasting Protocol for Wireless Sensor Networks 1139

supposed to initiate an interest packet dissemination throughout the entire network by

flooding. Then a node receiving the interest sets up a gradient which indicates from

whom this interest message has previously been forwarded. Although some additional

feature such as a gradient reinforcement has been proposed, the directed diffusion

with such a flooding of interest messages obviously increases network traffic and

leads inefficient energy consumption on sensor nodes.

A geographical propagation can be more useful than flooding when an interest

message needs to send towards a subset of sensor need within a certain region. Thus,

a geocasting can reduce the number of redundant packets by aid of the location

information of nodes. GEAR [4] is one of geocasting protocols for sensor networks. It

utilizes a greedy forwarding for the packet delivery toward the target region. In

greedy forwarding, a packet is forwarded to only one of the neighbor nodes whose

geographical location is closest to the destination. Therefore, GEAR can minimize

redundant packet traffic caused in flooding. However, most conventional geocasting

protocols including GEAR consider only a single target region. The problem we are

addressing in this paper is how to efficiently deliver interest messages to multiple

target regions so that the latency as well as the bandwidth consumption can be

reduced.

There are many sensor network applications, which require to collect the identical

information from multiple regions. For example, a monitoring system in hostile

environments may need to send the same advertisement to the sensors in the several

regions for changing the sensing mode or interval. It may also need to send some

queries such as “what’s the average temperature in each target region A, B and C?”.

Additionally, in the battle field, the command center can give the same query to the

sensors within multiple combat areas. Example queries for such scenarios would be,

“How many tanks or soldiers are observed in regions X, Y and Z?” or “Where are

tanks in regions X, Y and Z?”. For these applications, conventional protocols need to

send the identical interests to each target region multiple times. It causes significant

performance degradation by increasing network traffic and wasting the energy.

We propose a noble scheme that sends interest just once at the sink node instead of

multiple packet transmissions toward different target regions. Our scheme, named

FERMA, creates a suitable shared path among multiple target regions. The interest

messages are then forwarded along this path from the sink node to each target region

through an optimal junction point. To find such an optimal junction point, we utilize

the theorem of the “Fermat Point” [5]. After the interest reaches any one node in each

target region, local flooding starts inside the region. A gradient, which represents the

reverse path of the interest, is set up toward the sink node in the process of the interest

forwarding. This gradient is utilized for actual data deliveries from sensor nodes to

the sink node.

Our scheme also performs a data aggregation to reduce the amount of data traffic.

It is done at each Fermat Point and entrance nodes of local flooding inside the target

regions. The rest of the paper is organized as follows. Section 2 introduces the

theorem of Fermat Point and its proof. In Section 3, we examine our proposed scheme

in aspects of interest forwarding and data forwarding followed by ns-2 simulation

results in Section 4. We conclude in Section 5.

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1140 Y.-M. Song, S.-H. Lee, and Y.-B. Ko

2 Background and Motivation

2.1 Definition of the Fermat Point

First of all, we need to explain the theorem of Fermat Point which is important to

understand our scheme. Fermat point is the solution for the following question: what

is the point such that the sum of its distances from the vertices of a triangle is a

minimum? The definition of Fermat Point with a proof is following.

Definition. In any triangle ∆ABC, we can draw three equilateral triangles ∆A'BC,

∆B'CA, and ∆C'AB at the edges of ∆ABC as shown in Fig. 1(a). It is denoted by

Fermat Point, an intersection point of three straight lines,

which connects a vertex of the given triangle and a vertex of the opposite equilateral

triangle.

'

AA ,

'

BB and

'

CC , each of

Theorem. Fermat Point is the point such that the sum of its distances from the

vertices of a triangle is a minimum.

(a) (b)

Fig. 1. The definition of Fermat Point and its proof

Proof. In ∆ABC in Fig. 1(b), select a point P and connect it with vertices

A, B, and C. Rotate ∆ABP

°

60 around B into position ∆C'BP'. By construction,

∆BPP' is equilateral,

''PC PA =

,

PCPPPC PCPB PA

++=++

'''

. As the image of A under the rotation, position of C'

does not depend on P. Also,

PCPB PA

++

no shorter than the straight line

'

CC . Therefore,

if P lies on

'

CC . For this P, ∆ABC' is also equilateral because

°=∠

60'

ABC

. With similar methods, we can draw other straight lines which connect

vertices of the triangle with the opposite vertices of equilateral triangles. These

straight lines cross at one point. From the definition, this point is Fermat Point. Thus,

Fermat Point is the point such that the sum of its distances from the vertices of a

triangle is a minimum.

and

BPPB

'

=

. Thus, we have

'

CC

≥

because the broken line

PCPB PA

++

''C CPP

is

reaches its minimum

AB

=

BC

'

and

The construction of Fermat Point fails if one of the internal angles of ∆ABC is

more. Because Fermat Point is drawn outside of the triangle. In this case, the vertex

itself having the largest angle becomes an optimal point to reach each vertices of that

triangle.

°

120 or

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FERMA: An Efficient Geocasting Protocol for Wireless Sensor Networks 1141

Fig. 2. Fermat Point applied in Sensor Networks with multiple target regions

2.2 Applying Fermat Point Concept for Sensor Network Geocasting

We illustrate how to apply the theorem of Fermat Point in wireless sensor networks.

Suppose that the two points A and B of the given triangle in previous Fig. 1(b) are

the two central positions of the target regions X and Y, and then the point C is

assumed to be the sink node. In this environment, the virtual triangle with three

points is still formed as in Fig. 2. Therefore, we can calculate the Fermat point P,

and a certain node which is closest to the Fermat Point can play a role as the

junction point toward two target regions. From the sink node to this junction node,

interest messages are delivered through the shared path, and then they are separated

to each target region respectively. Thereby, we can optimize the interest forwarding

process.

The above technique can be generalized to any number of increasing target

regions as shown in Fig. 3. It may be possible to construct only one path curved

severely like a circle when many target regions are placed in around the sink node. In

this case, that path is extremely skewed and too long, so using such a path result in

inefficiency. To solve this problem, we divide target regions into three different

groups according to the angle made by them and the sink node. In Fig. 3(a), the

target regions 1, 2, and 3 belong to the first group, since the angles made by the sink

node and these regions do not exceed 120 degrees. In Fig. 3(b), and (c), the regions

4, 5 belong to the second group, since the angles made by the sink node and these

regions are in between 120 degrees and 240 degrees. In the same way, region 6

belongs to the third group. The three shared paths are set up with target regions in

each group respectively. Consequently, the interest messages initiated by sink node

are sent along to each path.

3 Proposed Scheme: FERMA

Our proposed scheme consists of two phases: interest forwarding phase and data

forwarding phase. To disseminate interest messages toward multiple regions, a sink

first creates a shared path based on the theorem of Fermat Point. Then, according to

this path, interest messages are delivered to each target region. Any node receiving

interest messages simultaneously sets up the corresponding gradient toward the

previous sender for data forwarding in the next stage. More details will follow.

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1142 Y.-M. Song, S.-H. Lee, and Y.-B. Ko

Fig. 3. Construction of the shared path in 360 degrees

3.1 Interest Message Forwarding Phase

For simplicity, let us consider only two target regions. Fig. 4 (a) illustrates a simple

greedy forwarding approach towards the two different target regions. Since there is no

optimization rule for multiple target regions in the pure greedy forwarding, the sink

node is required to send an interest towards target region A and then, again sends the

same interest message towards another target region B. When these interest packets

reach in the designated target regions, local flooding is triggered, which means that all

nodes within the target regions rebroadcast the receiving interests. Note that, as the

number of target regions increases, the frequency of interest message transmissions

by the sink also increases in this type of simple greedy approach.

(a) Simple Greedy forwarding (b) The proposed FERMA forwarding

Fig. 4. Comparison of Simple Greedy protocol and FERMA protocol

On the other hand, the proposed FERMA algorithm makes a virtual triangle with

three vertices including the sink node and two central points of the target regions as

mentioned in the previous section. From the definition of the Fermat Point theorem,

that point becomes the optimal point that minimizes the sum of distances from the