[ieee 2011 seventh international conference on mobile ad-hoc and sensor networks (msn) - beijing,...

Data Collection in Wireless Sensor Networks by utilizing multiple Mobile Nodes

Chao Wang

Beijing Key Lab of Intelligent Telecomm.Software and Multimedia

Beijing University of Posts and Telecomm.Beijing, China

Email: [email protected]

Huadong Ma

Beijing Key Lab of Intelligent Telecomm.Software and Multimedia

Beijing University of Posts and Telecomm.Beijing, China

Email: [email protected]

Abstract—Data collection is a fundamental and importantissue in wireless sensor networks (WSNs). Recent researchhas shown that using mobile nodes to collect and carry datain WSNs has many advantages over static multi-hop routing.In this paper, we focus on the problem of data collection inWSNs with the minimum mobile nodes. A mobile node canpick up the data cached in a sensor node via one-hop wirelesscommunications when it passes by a point that R meters awayfrom this stationary sensor node. Since the storage capability ofsensor node is limited, each mobile node must visit the sensornodes, that assigned to it, every t seconds to avoid the overflowof sensor data. In order to reduce the cost of mobile nodes,we try to minimize the number of mobile nodes. We formallyprove that the problem of minimizing the number of mobilenodes required by periodical data collection in WSNs is NPhard. We propose a path planning algorithm to minimize thenumber of mobile nodes. Our simulation results show that ourapproach can notably reduce the number of required mobilenodes as much as 55.6%.

Keywords-wireless sensor network, mobile node, data collec-tion.

I. INTRODUCTION

Recent technological advances have enabled the produc-

tion of low-cost sensor nodes [1]. The proliferation of

low-cost tiny wireless sensor nodes (such as the Berkeley

Mote [2]) and their unattended nature of operation make

wireless sensor networks (WSNs) an attractive tool for

extracting and gathering data by sensing real-world phe-

nomena from the physical environment. It has been widely

used in numerous applications, ranging from environment

surveillance [3], scientific observation [4]–[6], object track-

ing, to structure monitoring [7]. For these applications, data

collection is a fundamental and very important task and

data collected by stationary sensor nodes is required to be

transferred to a central location for further analysis [14].

Within the past decade, many researchers have proposed

using mobile nodes as a solution of data collection for

WSNs [8]–[13], [16]. Mobile nodes can pick up cached data

from stationary sensor nodes when they come near them and

transfer the date to the base station.

Comparing with the ad-hoc multi-hop forwarding pattern,

mobile nodes assisted data collection has many advantages.

(a) (b)

Figure 1: Data collection by using multiple mobile nodes

In ad-hoc multi-hop forwarding WSNs, data is transferred

from each sensor node to a fixed base station by using

multi-hop routing. In this case, the well known problem of

“hot spots” occurs. Namely, sensor nodes closer to the base

station relay most of the data and exhaust their energy more

quickly, leaving the network disconnected [15]. By utilizing

mobile nodes, data can be transferred to the base station

via mobile nodes. This naturally avoids the ad-hoc multi-

hop forwarding pattern and removes the relaying overhead

of sensor nodes near the base station. Furthermore, the

stationary sensor nodes no longer need to build a connected

wireless network when mobile nodes are used to collect

data. Thus the deployment of WSNs can only take the

sensing requirement into account, without considering the

connectivity of the wireless network. Hence, mobile nodes

present an attractive alternative to multi-hop forwarding for

efficient data collection in WSNs.

In this paper, we consider the problem of data collection

in WSNs with the minimum mobile nodes. A mobile node

can pick up data cached on a stationary sensor node via one-

hop wireless communications when it pass by a point that

R meters away from this stationary sensor node. R is the

maximum communication distance between a mobile node

and a stationary sensor node. Each stationary sensor node

that deployed in the monitoring area has limited storage

capability and can cache its data for at most t seconds. Wecall a stationary sensor node is visited by a mobile node,

if the cached data of this sensor node is picked up by a

mobile node. Each stationary sensor node should be visited

2011 Seventh International Conference on Mobile Ad-hoc and Sensor Networks

978-0-7695-4610-0/11 $26.00 © 2011 IEEE

DOI 10.1109/MSN.2011.32

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978-0-7695-4610-0/11 $26.00 © 2011 IEEE

DOI 10.1109/MSN.2011.32

83


978-0-7695-4610-0/11 $26.00 © 2011 IEEE

DOI 10.1109/MSN.2011.32

83

by a mobile node at least once every t seconds to avoid dataoverflow, which is featured as t-visit. If the moving speed of

mobile node is fast enough, we can use only one mobile node

to visit all sensor nodes within t seconds. In practice, themoving speed of mobile node is limited. Therefore, multiple

mobile nodes are required to to make sure all sensor nodes

are t-visited. For example, in Figure 1(a), four mobile nodes

are required to visit all sensor nodes within a pre-specified

t-visit period t. Each mobile node moves along its travelpath and visits the set of sensor nodes that assigned to it.

When multiple mobile nodes are used to provide t-visit,

the number of mobile nodes should be minimized to reduce

the cost of WSNs since minimizing the number of mobile

nodes can reduce the cost of buying mobile nodes. For

instance, in Figure 1(b), 3 mobile nodes are sufficient to visit

all sensor nodes, which is fewer than that in Figure 1(a). The

number of mobile nodes required by t-visit is related to the

travel paths of mobile nodes. We try to reduce the number of

mobile nodes by carefully designing the travel path of each

mobile node. The contributions of this paper can be summa-

rized as follows. First, we formally model the problem of

global t-visit via one-hop wireless communications with the

minimum mobile nodes and prove that it is NP hard. Second,

we propose a heuristic path planning algorithm to minimize

the number of mobile nodes and optimize their travel paths.

Finally, we evaluate the proposed scheme by simulation.

The simulation results demonstrate that our scheme can

remarkably reduce the number of mobile nodes, compared

with existing approaches.

The rest of the paper is organized as follows: Section II

briefly discusses the related works. Section III introduces the

global t-visit with the minimum mobile nodes problem and

proves that the global t-visit with the minimum mobile nodes

problem is NP-hard. In section IV, we analyze what kind of

travel path can make a mobile node visit more sensor nodes

within a t-scan period. Our path planning algorithm which

tries to reduce the number of mobile nodes is presented

in section V. Section VI evaluates the performance of our

algorithm. Finally, we conclude our paper in section VI.

II. RELATED WORK

Many works have been proposed to exploit mobility in

WSNs. Motivated by the observation of “hot spots”, many

works [9], [15] propose to use mobile base stations to

achieve balanced energy consumption. They find that the

perimeter of the sensing filed is the optimal path for base

station. Since the location of the base stations is change

dynamically, additional overhead is brought by maintaining

efficient network topology and routing information.

In some works, mobile nodes pick up data generated by

sensor nodes via one-hop wireless communications. In [19],

shah et al proposed a three-tier architecture with mobile

entities called Data Mobile Ubiquitous LAN Extensions

(MULEs). Data MULEs randomly travel within the monitor-

ing area and pick up cached data from nearby sensor nodes.

The gathered data are deposited at the wired access point.

In [18], Cheng et al. propose a centralized path planning

algorithm, CSWEEP, for mobile nodes which are used to

periodically collect data of all interested points. CSWEEP

first generated an approximate TSP ring by using the PTAS

algorithm of traveling salesman problem (TSP). Then the

TSP ring is divided into several segments. Each mobile node

moves continuously on one specific segment back and forth

for collecting data from the interested points on its path. For

both [18], [19], their travel paths for mobile nodes are not

optimal.

Multi-hop network transmissions and the movement of

mobile node are jointly considered in some works. In [12],

[17], [20], the data are sent from the source to the sensor

nodes with only one hop away from the path of mobile

node. The mobile node then picks up the cached data when

it passes by. In [22], Wang et al. find that the network

lifetime can be maximized by constrain the movement of

mobile node in the vicinity of the base station. This kind

of works can not avoid the non-uniform depletion of sensor

node energy and the sensor nodes near the path of mobile

nodes are the first to run out of batteries.

The multiple traveling salesman problem (mTSP) [21]

and Traveling Salesman Problem with Neighborhoods

(TSPN) [25], where the neighborhoods are the disks around

each sensor, are closely related to the problem we study

here. The mTSP problem consists of determining a set of

routes for m salesmen who all start from and turn back to a

home city. The TSPN try to find a tour of minimum length

that connects all disks. But, they both are different from our

problem. First, our work tries to use multiple mobile nodes

to visit all sensor nodes within pre-specified time constrain.

Both mTSP and TSPN have no time constrain. Second,

TSPN generate only one tour, but we generate multiple

paths. Third, the paths generated by our algorithm don’t like

the paths of mTSP that start and end at the same point.

III. GLOBAL T-VISIT

In this section, we first give some definitions related to

global t-visit. Then, we present the formal definition of

global t-visit with the minimum number of mobile nodes.

Finally, we prove the NP hardness of determining the

minimum number of mobile nodes required by global t-visit.

The used notations in this paper are summarized in Table 1.

A. Definition of global t-visit

A sensor network S, that consists of a collection of nstationary sensor nodes {s1, s2, . . . , sn}, is deployed withina 2D plane. Each sensor node is assigned an unique ID.

All sensor nodes can obtain their locations by using GPS

or some localization technologies like [23]. We also assume

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Table I: Used notations

Notation MeaningS A sensor network consists of a collection of n sensor nodes

si The sensor node with node ID i

K The number of mobile nodes

mi The mobile node with node ID i

v The maximal moving speed of mobile nodes

R The transmission radius of sensor nodes

t The time of a t-visit period

Pi The travel path of mobile node mi

|Pi| The length of path Pi

L The maximal travel length of mobile node within a t-scanperiod

hi A visit point of sensor node si

oi A disk centered at sensor node si with radius R

dij The distance between visit point hi and jj

that each sensor node is equipped with an omnidirectional

antenna and the transmission/reception area of each sensor

node is roughly a disk centered at the sensor node. All the

sensor nodes have the same transmission radius denoted as

R. A mobile node can communicated with a sensor node

when the distance between them is no more than R meters.

Therefore, the sensor network S = {s1, s2, . . . , sn} can bemodeled as a disk set, denoted as O = {o1, o2, . . . , on},deployed within a 2D plane. This follows the unit disk graph

model in [26]. If the data stored on sensor node si is pickedup by mobile node mj when mj passes by a point hi on the

edge of disk oi, we say sensor node si is visited by mobilenode mj . We call this point hj visiting point. In practice,

the storage capability of sensor node is limited and each

sensor node can locally cache its data for at most t seconds.Therefore, each sensor node must be visited by a mobile

node at least once every t seconds to avoid the overflow of

sensed data. Now, we can get the definition of t-visit.

Definition 1. T-visit: A sensor node is said to be t-visited ifand only if the data cached in this sensor node is picked upby a mobile node at least once for every t seconds. Here, tis the time of a t-visit period. The t-visit period t depends onthe application and the storage capability of sensor node.

We also assume that all mobile nodes know the location

and ID of each sensor node. It is also reasonable to suppose

that mobile nodes are rechargeable and the storage capac-

ity of each mobile node is assumed to be sufficient. Let

M = {m1,m2, . . . ,mk} be the set of mobile nodes that beutilized to collect data, where K is the number of mobile

nodes. Each mobile node periodically travels along the same

path to visit the sensor nodes assigned to it. Let v be themaximal moving speed of a mobile node, the path length of

each mobile node should be less than L = v × t. Based onthe definition of t-visit, we can get the definition of global

t-visit.

Definition 2. Global t-visit: We define the global t-visit of

a WSNs S as the situation that all sensor nodes of S is t-visited. In other words, each sensor node of S is visited bya mobile node at least once every t seconds.

B. Global t-visit with the minimum mobile nodes

In order to achieve global t-visit, we need to send out

several mobile nodes to make sure that every sensor node

is visited by a mobile node at least once for each t-visit

period. The most fundamental problem we concern is, given

a sensor network S, what is the minimum number of mobile

node to achieve Global t-visit. We call this problem global

t-visit with the minimum mobile nodes problem (GTVM).

Let U = {u1, u2, . . . , uK} be a partition of disk set O and

P = {P1, P2, . . . , PK} be a path set. Mobile node mi can

visits all disk that belong to cell ui by traveling along path

Pi. If for each Pi ∈ P, the length of path Pi, denoted as|Pi|,is no more than v × t, P is a feasible solution for global t-visit. The GTVM can be formally defined as:

Obj. minimizeU∈U |U |s.t.

|Pi| � v × t, ∀Pi ∈ P, (1)

where U is the set of all possible partition of disk set O.Formula (1) implies that each mobile node can visit all

mobile assigned to it within a t-visit period.

Lemma 1. The global t-visit with the minimum mobile nodesproblem is NP-hard.

Proof: We first show that the GTVM ∈ NP . LetP1, P2, . . . , Pk are the travel paths of k mobile nodes. A

verification algorithm can check whether all sensor nodes in

S are visited by a mobile node for each t-visit period and

the path length of each mobile node does not exceed the

maximal travel length L = v × t. Since the number of pathand sensor node are finite, the verification can be done in a

polynomial time. Therefore, the GTVM ∈ NP .To prove that the decision version of the GTVM is NP-

hard, we show a polynomial time reduction from the NP-

hard problem - Traveling Salesman Problem with Neighbor-

hoods (TSPN) [25] to the GTVM.

Given a set of n disks with radius R, denoted as O ={o1, o2, . . . , ok}, in a 2D plane, the TSPN seeks the shortest

path to visit all disks at least once. The corresponding

decision version of the TSPN is whether there is a path

with length no more than the maximal travel length L. Ifthe TSPN problem has a solution to visit all disks in Owith length no more than the maximal travel length L, onemobile node is enough to provide global t-scan: the path for

the TSPN problem is the travel path of the mobile node and

all sensor node can be visited at least once every L/v = tseconds. On the other hand, if GTVM has a solution of one

mobile node, this solution is also a solution for the decision

problem of the TSPN. Because, for each t-scan period, each

sensor node must be visited by the mobile node at least once.

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The total length of this path is at most v×t = L. Hence, thetravel path of the mobile node is also a path for the TSPN

problem that all disks are visited at least once. This proves

that the GTVM is NP-hard.

IV. TRAVEL PATH OF MOBILE NODE

Since the travel speed of a mobile node is limited, multiple

mobile nodes are required by achieving global t-visit. If a

mobile node can visit more sensor nodes within a t-scan

period, less mobile nodes are required by global t-scan. We

find that the travel path pattern of mobile node can affect the

number of sensor node that a mobile node can visit within

a t-scan period. In this section, we study what kind of travel

path can make a mobile node visit more sensor nodes within

a t-scan period.

Lemma 2. Let us consider the scenario that a mobile nodecollects data by moving along the same travel path in eacht-visit period. If a mobile node travels along a loop, it canvisit more sensor nodes within a t-scan period by comparingwith traveling along a non-loop path.

Proof: Since a mobile node must visit all sensor nodesassigned to it, it must set out from one visit point of a sensor

node that assigned to it and go back to this visit point after

visiting all other sensor nodes assigned to it. All this must

be done within a t-visit period. Suppose, within a t-visit

period, a mobile node starts it travel from visit point hi of

sensor node si and returns to hi after reaching visit point hj

of sensor node sj . Let Rij be the path that a mobile node

moves from hi to hj via some other visit points and |Rij |is the length of Rij. Let lij be the straight line from hi to

hj and dij be the length of lij .Non-loop travel path. If the travel path is a Non-loop

travel path, the mobile node must backtrack to hi along the

same trajectory that it travels from hi to hj . In this case,

the travel path is hiRij−−→ hj

Rji−−→ hi. The total length of

the travel path is L1 = |Rij |+ |Rji| = 2|Rij |. For example,in Figure 4(a), the mobile node moves from h1 to h5 alongh1 → h2 → h3 → h5, then back to h5 along h5 → h3 →h2 → h1.Loop travel path. If the travel path is a loop, the mobile

node can move back to hi along lij directly after arrivingat hj . In this case, the travel path of the mobile node is

hiRij−−→ hj

lji−→ hi. The total length of this travel path is

L2 = |Rij | + |lji|. For example, in Figure 4(a),the travelpath is h1 → h2 → h3 → h5 → h1.In a 2D plane, as we known, the straight line is the shortest

path among all possible paths between two points. Therefore,

we can get |lji| � |Rij |. Then, L1 = |Rij |+ |Rji| � |Rij |+|lji| = L2. Finally, we can get that L2 � L1. This means the

mobile node has potential to move farther with the distance

of L1 −L2 � 0 and to visit more sensor nodes. Figure 4(b)

12

3

5

4

1

h2

h3

h5Sensor nodeVisit point(a) Non-loop

12

3

5

4

1

h2

h3

h5Sensor nodeVisit point

h4

(b) loop

Figure 2: Traveling along a loop or not

gives us an example of this scenario. When the mobile node

returns to h1, it can visit h4 without breaking the travel pathlength constraint. In this way, it can visit 5 sensor nodes,

which is more than the case in Figure 4(a). Lemma 2 is

proved.

Lemma 2 shows that a mobile node that moves along a

loop travel path can visit more sensor nodes. In the following

section, we will propose a heuristic path planning algorithm

which try to reduce the number of mobile nodes required

by global t-visit by utilizing Lemma 2.

V. THE PATH PLANNING ALGORITHM

Since determining the minimum number of mobile node

required by global t-visit is NP-hard, we present a heuris-

tic path planning algorithm called LoopGrowth to reduce

the number of mobile nodes required by global t-visit. In

LoopGrowth, if a sensor node is assigned to a mobile node,

we say this sensor node is covered. For each iteration of

LoopGrowth, a mobile node is added into the monitoring

area to cover more sensor nodes until all sensor nodes are

covered. The travel path of the newly added mobile node

is extended by continuously assigning uncovered sensor

node to this mobile node until the length of the travel path

reaches the maximum path length. By Lemma 2, a mobile

node can visit more sensor node by traveling along a loop.

LoopGrowth reduces the number of mobile nodes required

by global t-visit by guaranteeing the travel path of each

mobile node is a loop. Before introducing the details of

LoopGrowth, we first introduce some basic definitions used

in LoopGrowth.

Definition 3. Seeded sensor node: Assume that all un-covered sensor nodes are distributed in a 2D plane. Alluncovered sensor nodes can be contained in a rectangle.The sensor node which is closest to the left-bottom rectanglevertex is called seeded sensor node.

When a new mobile node is added into the monitoring

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1 2

34

1

h2h3h4

Sensor nodeVisit point

5

6

Figure 3: Extendable sensor node of a path.

area, it will cover the seeded sensor node at first and choose

a point on the edge of the transmission/reception area of this

sensor node as the start point of its travel path. Using this

approach, LoopGrowth can avoid the case that the uncovered

sensor nodes are separated by the paths of the added mobile

nodes. If this happens, more mobile nodes are required to

achieve global t-visit.

We define the path segment as the part of path between

two adjacent visit points of a travel path. If LoopGrowth

assigns an uncovered sensor node to the newly added mobile,

the mobile node has to extend its travel path to cover this

uncovered sensor node. We define the path increment as the

part of path length increased by inserting a visit point into a

path segment. For example, in Figure 3, the path increment

of sensor node s4 for E31 is Δ431 = d34 + d41 − d31. Forany arbitrary path segment Eij , we define the extendable

sensor node of Eij as the uncovered sensor node with the

minimum path increment for Eij . For example, in Figure 3,

sensor node s4 has the minimum path increment for E31.

Therefore, sensor node s4 is the extendable sensor node ofE31.

Definition 4. Path increment: Let Eij be the path segmentbetween two adjacent visit points hi and hj on travel pathPi and dij be the distance between point hi and hk. Let hk

be a point on disk ok and the sum of the distances from hk

to hi and hj , denoted as (dik + djk), is smaller than thatof any other points on disk ok. If we assign sensor node skto mobile node mi and insert a point on disk ok into pathsegment Eij , we would like to insert hk between hi and hj

to minimize the increased path length. The path segment−→ij

becomes two path segments−→ikj. The increased path length

is dik + dkj − dij . We define the path increment of sensornode sk for Eij as Δkij = dik + dkj − dij .

Definition 5. Extendable sensor node: Let Eij be a pathsegment of travel path Pi. We define the extendable sensornode of path segment Eij as the uncovered sensor node withthe minimum path increment for edge Eij . The related visitpoint hi that minimizes the path increment is defined as pathextending point for Eij .

Algorithm 1 The LoopGrowth algorithm1: K = 0,P = ∅, S = ∅

2: Initialize path P to be ∅; Initialize path length L to be

0; Initialize the sensor node set SS that assigned to the

newly added mobile node to be ∅;

3: Find the seeded sensor node SN ; Add SN into SS and

remove SN from S;4: Set s be the closest sensor node to SN . Add s into SSand remove s from S;

5: Find the shortest line that connects the communication

disks of SN and s. Add the two endpoint of this lineinto the path P ; L is set to be the length of this line;

6: Find the extendable sensor node and corresponding path

extending point for each path segment; Store these

information for each path segment;

7: if Existing extendable sensor node then8: s=the extendable sensor node with the minimum path

increment among all extendable sensor nodes;

9: if (L+Δs) � (v × t) then10: Add s into SS and remove s from S;11: Insert path extending point of s into the path P ;12: L = L+Δs;

13: Update the extendable sensor node and correspond-

ing path extending point for the path segments with

invalid extendable sensor node;

14: goto 7;

15: else16: P = P ∪ P ;S = S ∪ SS;K = K + 1;17: goto 3;

18: end if19: else20: return K;

21: end if

If the length of the travel path of the newly added

mobile node is less than the maximum travel length (v× t),LoopGrowth will try to extend this path by assigning the

extendable sensor node with the minimum path increment

among all extendable sensor nodes to the newly added

mobile node. For example, in Figure 3, the path increment

sensor node s4 is smaller than that of sensor node s5 andsensor node s6. Therefore, LoopGrowth assigns sensor nodes4 to the newly added mobile node and inserts the visit pointh4 into the travel path of this mobile node by changing the

path segment−−→h3h1 into

−−−−→h3h4h1.

The details of LoopGrowth are shown in Algorithm 1. In

each iteration, LoopGrowth adds one mobile node into the

monitoring area and finds a travel path for it. LoopGrowth

stops until each sensor node is assigned to a mobile node.

At the beginning of each iteration, the seeded sensor node

is assigned to the newly added mobile node at first (line

4). Then, the travel path of the newly added mobile node

is set to be the shortest line segment that connects the

communication disks of the seeded sensor node and the

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0 200 400 600 800 10000

200

400

600

800

1000

Figure 4: Travel paths generated by LoopGrowth.

closest sensor node to the seeded sensor node (line 5).

LoopGrowth continuously assigns sensor node with the

minimum path increment among all extendable sensor nodes

to the newly added mobile node (line 10). The travel path is

extended by inserting the corresponding path extending point

of the newly assign sensor into it if its length is no more

than the maximum travel length (v × t) (line 13). The pathextending point is inserted between two adjacent visit points

to make sure the travel path of the mobile node is a loop. If

the newly generated travel path reaches the maximum travel

length (v × t), a new mobile node will be added into the

monitoring area unless all sensor node is assigned (line 16).

VI. PERFORMANCE EVALUATION

In this section, we extensively validate the performance

of our path planning algorithm LoopGrowth via simulation

running on a computer with 2.4 GHz and 1 GB memory.

Comparing with existing works, our simulations demonstrate

that LoopGrowth can notably reduce the number of mobile

nodes required by global t-visit.

A. Efficiency of LoopGrowth

We first evaluate the performance of LoopGrowth in terms

of the number of mobile nodes required by global t-visit

and the total travel travel length of all mobile nodes. Since

no similar work has considered the communication distance

between the mobile nodes and the sensor nodes, we compare

LoopGrowth with CSWEEP [18] which is close to our

works. CSWEEP uses multiple mobile nodes to visit all

interested points periodically. The travel path of each mobile

node in CSWEEP is a segment of the TSP ring and each

mobile node returns to the start point of its travel path by

backtracking along the same path. Therefore, the travel paths

of mobile nodes in CSWEEP are non-loop travel path.

In our simulation, 100 sensor nodes, represented as red

dots in Figrure 4, are randomly deployed in a 1000meters×1000 meters square area. When a mobile node reaches

the edge of a disk, it can pick up the data cached on

the sensor node in the center of the disk. The maximum

0 200 400 600 800 10000

200

400

600

800

1000

Figure 5: Travel paths generated by CSWEEP.

moving speed of mobile nodes is set to 0.5m/s. We assumethat the move speed of mobile nodes can be adjusted

according the requirement. Figure 4 shows an example of

the travel paths of mobile nodes generated by LoopGrowth.

The transmission radius is set to be 20 meters and the t-visit period is set to be 1500 seconds. The lines represent thetravel paths of mobile nodes, and each closed loop means

a travel path of one mobile node within a t-visit period.

The yellow dots are the visit points. We can see that 11

mobile nodes are required to achieve global t-visit by using

LoopGrowth.

We also implement CSWEEP according to the description

in [18]. The evaluation settings used in CSWEEP are the

same as that used in LoopGrowth. The TSP travel path

is computed by using the well-known TSP solver Con-corde [24]. Figrure 5 shows the result of CSWEEP. In

Figrure 5, the dots and squares both indicate the deployed

sensor nodes. The line segment between any two adjacent

squares is a travel path for a mobile node. Within one visit

period, each Mobile node moves from one square to the

next one and then backtracks to the start one. Therefore,

the maximum distance between any two adjacent squares is

no more than (v × t)/2 = (0.5× 1500)/2 = 375(meters).In Figrure 5, we can see that 24 mobile nodes are required

to achieve global t-visit by using CSWEEP algorithm. It is

very clear that CSWEEP requires more mobile nodes than

LoopGrowth.

In order to more clearly study the number of mobile

nodes require by LoopGrowth and CSWEEP, we vary the

time of t-visit period t from 1200 seconds to 4400 seconds.For each value of t, we repeat the simulation 10 times

and compute the average number of mobile node required

by LoopGrowth and CSWEEP respectively. The simulation

results are shown by Figrure 6. We can see that, compared

with CSWEEP, LoopGrowth can achieve global t-visit with

less mobile nodes in all cases of t-visit period. When the

t-visit period is set to be 1200 seconds, LoopGrowth canachieve global t-visit with about 16 mobile nodes. But about

36 mobile nodes are required by CSWEEP. The increase of

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1000 1500 2000 2500 3000 3500 4000 45000

5

10

15

20

25

30

35

40

t-visit period t

Num

ber o

f Mob

ile N

odes

LoopGrowthCSWEEP

Figure 6: The number of mobile nodes requried by Loop-

Growth and CSWEEP for varying t-visit period.

1000 1500 2000 2500 3000 3500 4000 45000

3000

6000

9000

12000

15000

t-visit period t

Tota

l tra

vel l

engt

h

LoopGrowthCSWEEP

Figure 7: The total travel length of LoopGrowth and

CSWEEP for varying t-visit period.

t-visit period t reduces the number of mobile nodes requiredby both LoopGrowth and CSWEEP, since the length of the

travel path of mobile nodes increases with t-visit period t.The number of mobile nodes required by them both drop

dramatically with the increase of the value t until t reaches3000 seconds. Hence, we can conclude that LoopGrowthcan achieve global t-scan with less mobile nodes in all

cases of t-scan period. This is because that mobile nodes in

LoopGrowth is travel along loop path which is more efficient

than non-loop travel path.

Next, we study the total travel length of all mobile nodes

of LoopGrowth and CSWEEP. The energy costed by the

movement of mobile nodes is increase with the total length

of their travel paths. For the same sensor network, the algo-

rithm with less total travel length is more energy efficient.

The total travel length of LoopGrowth and CSWEEP are

shown in Figrure 7. We can see that the total travel length of

CSWEEP is much bigger than that of LoopGrowth. This is

in accordance with the results in Figrure 6 that LoopGrowth

require less mobile node than CSWEEP. The total travel

path length of CSWEEP is about twice as much as that of

LoopGrowth when the t-visit period t is 4200. One reasonis that, for each t-visit period, mobile nodes in CSWEEP

must backtrack to the start points of their travel paths along

1000 1500 2000 2500 3000 3500 4000 45000

5

10

15

20

25

t-visit period t

Num

ber o

f Mob

ile N

odes

1000x10001200x12001400x14001600x1600

Figure 8: The number of mobile nodes requried by Loop-

Growth for varying sensor node density.

the same routes they used to visit the sensor nodes assigned

to them. The other one is that LoopGrowth considers the

communication distance between the mobile node and sensor

node. Hence, we can conclude that the total travel length of

LoopGrowth is less than that of CSWEEP in all cases of

t-scan period.

B. Impact of sensor node density

The following simulations focus on studying the impact of

sensor node density on the number of mobile nodes required

by LoopGrowth. In order to study the impact of sensor node

density, we randomly deploy 100 sensor nodes in four differ-

ent square areas with size of 1000 meters× 1000 meters,1200 meters×1200 meters, 1400 meters×1400 metersand 1600 meters× 1600 meters respectively. We vary thetime of t-visit period from 1200 seconds to 4400 seconds.

The rest settings of our simulations are the same as the

settings of the simulation in previous subsection. We run

each simulation 10 times and compute the average result.

The number of mobile nodes required by LoopGrowth

for varying sensor node density is shown in Figrure 8.

We can see that the number of mobile nodes required by

LoopGrowth increases with the size of the deployment area.

This is because the distances between sensor nodes increase

against the sensor node density. The maximum travel path

length of mobile nodes is pre-determine by the time of t-visit

period and the maximum moving speed of mobile nodes.

The increase of distances between sensor nodes can reduce

the number of sensor nodes that a mobile node can visit

within a t-visit period. Since the number of sensor node is

not changed in our simulations, increasing the size of deploy

area can reduce the sensor node density. Therefore, we can

conclude that the increase of sensor node density results in

the decrease of the number of mobile nodes required by

global t-visit.

VII. CONCLUSION

In this paper, we study the problem of data collection

in WSNs with minimum mobile nodes and optimizing the

paths of these mobile nodes, which is called global t-visit

898989

with the minimum mobile nodes problem. We propose a

path planning algorithm to minimize the number of required

mobile nodes by optimizing the travel path of each mobile

node. The simulation results show that our approach can

greatly reduce the number of mobile nodes as much as

55.6% by comparing with existing works.

ACKNOWLEDGMENT

The research reported in this paper is supported in part

by the National Basic Research Program of China (973 Pro-

gram) under Grant No.2011CB302701, the National Natural

Science Foundation of China under Grants No. 60833009,

and the National Science Funds for Distinguished Young

Scientists under Grant No.60925010.

REFERENCES

[1] K. Yuen, B. Liang, and B. Li. A Distributed Frameworkfor Correlated Data Gathering in Sensor Networks, IEEETransactions on Vehicular Technology, Vol. 57, No. 1, 2008.

[2] D. Estrin, D. Culler, K. Pister, and G. Sukhatme. Connectingthe Physical World with Pervasive Networks, IEEE PervasiveComputing, Vol. 1, No. 1, 2002.

[3] G. Tolle, J. Polastre, R. Szewczyk, D. Culler, N. Turner, K.Tu, S. Burgess, T. Dawson, P. Buonadonna, D. Gay, and W.Hong. A Macroscope in the Red woods, in Proc. of ACMSenSys, 2005.

[4] G. Werner-Allen, K. Lorincz, J. Johnson, J. Lees, and M.Welsh. Fidelity and Yield in a Volcano Monitoring SensorNetwork, in Proc. OSDI, 2006

[5] L. Mo, Y. He, Y. Liu, J. Zhao, S. Tang, X. Li, G. Dai. CanopyClosure Estimates with GreenOrbs: Sustainable Sensing in theForest, in Proc. of ACM SenSys, 2009.

[6] The GreenOrbs project. http://www.greenorbs.org.

[7] N. Xu, S. Rangwala, K. K. Chintalapudi, D. Ganesan, A.Broad, R. Govindan, and D. Estrin. A wireless sensor networkfor structural monitoring, in Proc. of ACM SenSys, 2004

[8] G. D. Celik and E. Modiano. Random Access WirelessNetworks with Controlled Mobility, In Proc. of IFIP MED-HOCNET, 2009.

[9] S. R. Gandham, M. Dawande, R. Prakash, and S. Venkatesan.Energy Efficient Schemes for Wireless Sensor Networks WithMultiple Mobile Base Stations, In Proc. of IEEE GLOBE-COM, 2003.

[10] R. Sugihara and R. Gupta. Optimizing Energy-Latency Trade-off in Sensor Networks with Controlled Mobility, In Proc. ofIEEE INFOCOM, 2009.

[11] M. M. Tariq, M. Ammar, and E. Zegura. Message ferry routedesign for sparse ad hoc networks with mobile nodes, In Proc.of ACM MobiHoc, 2006.

[12] G. Xing, T. Wang, Z. Xie and W. Jia. Rendezvous Planningin Wireless Sensor Networks with Mobile Elements, IEEETransactions on Mobile Computing, Vol 7, No 12, 2008.

[13] R. Sugihara and R. Gupta. Optimal Speed Control of MobileNode for Data Collection in Sensor Networks, IEEE Trans-actions on Mobile Computing, VOL. 9, NO. 1, 2010.

[14] C Wang, H Ma, Y He and S Xiong. Approximate DataCollection for Wireless Sensor Networks, In Proc. of IEEEICPADS, 2010.

[15] J. Luo and J.P. Hubaux, Joint mobility and routing for lifetimeelongation in wireless sensor networks, In Proc. of IEEEINFOCOM, 2005.

[16] A. A. Somasundara, A. Ramamoorthy, and M. B. Srivastava.Mobile Element Scheduling for Efficient Data Collection inWireless Sensor Networks with Dynamic Deadlines, In Proc.of IEEE RTSS, 2004.

[17] A. A. Somasundara, A. Kansal, D. Jea, D. Estrin, and M.B. Srivastava. Controllably mobile infrastructure for lowenergy embedded networks, IEEE Transactions on MobileComputing, Nol. 5, No 8. 2006.

[18] W. Cheng, M. Li, K. Liu, Y. Liu, X. Li, and X. Liao. SweepCoverage with Mobile Sensors, In Proc. of IEEE IPDPS,2008.

[19] R.C. Shah, S. Roy, S. Jain, and W. Brunette. DataMULEs:Modeling a Three-Tier Architecture for Sparse Sen-sor Networks, In Proc. of IEEE SNPA, 2003.

[20] D. Jea, A. A. Somasundara, and M. B. Srivastava. Multiplecontrolled mobile elements (data mules) for data collectionin sensor networks. In In Proc. of IEEE DCOSS, 2005.

[21] T. Bektas. The multiple traveling salesman problem: anoverview of formulations and solution procedures, Omega,Vol. 34, No. 3, 2006.

[22] W. Wang, V. Srinivasan, and K.-C. Chua. Using mobile relaysto prolong the lifetime of wireless sensor networks. In Proc.of ACM MobiCom, 2005.

[23] Z. Yang and Y. Liu. Quality of Trilateration: Confidencebased Iterative Localization, IEEE Transactions on Paralleland Distributed Systems, Vol. 21, No. 5, 2010.

[24] http://www.tsp.gatech.edu/concorde.html.

[25] K. Elbassioni, A. V. Fishkin, and R. Sitters.ApproximationAlgorithms for the Euclidean Traveling Salesman Problemwith Discrete and Continuous Neighborhoods, InternationalJournal of Computational Geometry and Applications, Vol.19, NO. 2, 2009.

[26] B. N. Clark, C. J. Colbourn, and D. S. Johnson. Unit diskgraphs. In Discrete Mathematics, Vol. 86, pages 165C177,1990.

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