research article an adaptive aggregation scheduling algorithm based...

Research ArticleAn Adaptive Aggregation Scheduling Algorithm Based onthe Grid Partition in Large-Scale Wireless Sensor Networks

Xiaogang Qi,1 Lifang Liu,2 Gengzhong Zheng,3 and Mande Xie4

1School of Mathematics and Statistics, Xidian University, Xi’an 710071, China2School of Computer Science and Technology, Xidian University, Xi’an 710071, China3School of Computer Science and Engineering, Hanshan Normal University, Chaozhou 521041, China4College of Computer and Information Engineering, Zhejiang Gongshang University, Hangzhou 310018, China

Correspondence should be addressed to Lifang Liu; [email protected]

Received 8 May 2015; Accepted 16 July 2015

Academic Editor: Jianping He

Copyright © 2015 Xiaogang Qi et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Data aggregation algorithm aims to reduce the redundant information by gathering the sensed data, save energy, and prolong thelifetime of the network. However, the data aggregation technology will increase the network transmission delay of wireless sensornetworks. Minimum-latency aggregation scheduling is designed to minimize the number of scheduled time slots to perform anaggregation. In this paper, we present an Adaptive Aggregation Scheduling Algorithm based on the Grid Partition (AASA-GP) inlarge-scale wireless sensor networks. By dividing the network into grids based on the geographical information, we allocate thechannels according to the grid coordinates. Nodes with the same grid coordinates use the same channel and the adjacent grids usethe different channels, so we can effectively avoid the wireless media transmission interference, increase the parallel transfer rate,and reduce the aggregation latency. Our extensive evaluation results demonstrate the superiority of the AASA-GP. For small-scalenetworks, the resultant latency is comparable with the best practice, and it is more suitable for large-scale wireless sensor networks.

1. Introduction

In multihop wireless sensor networks, a fundamental task isto gather data from all sensors to a distinguished sink node [1,2]. It is already noted that adjacent sensor nodes monitoringan environmental feature typically register similar values[3]. This data redundancy of the spatial correlation amongsensor observations inspires the research of in-network dataaggregation. In general, each intermediate node aggregates itsreceived data with its own record according to some aggre-gation functions (e.g., taking the maximum or minimumof them) into a single packet with fixed size. This type ofapplication is called data aggregation, and its communicationpattern is called convergecast [4]. The naive aggregationapproaches which purely rely on medium-access-controllayer mechanisms could result in latency that is too highto be practical due to the existence of mutual transmissioninterference [5, 6]. The goal of our study is to minimize the

average data aggregation latency of the convergecast process,and a synchronized aggregation scheduling is necessary,where all transmissions proceed in synchronous time slots.Such an aggregation scheduling is designed under threeconditions:

(1) Each node transmits atmost one packet with the fixedsize in its allocated time slot.

(2) A node cannot transmit until all of its childrencomplete the transmissions to itself.

(3) The assigned transmissions in the same time slotshould be interference-free.

In this paper, the latency is measured by the number of timeslots of the whole aggregation convergecast process, and ourgoal aims to minimize the latency.

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2015, Article ID 283209, 9 pageshttp://dx.doi.org/10.1155/2015/283209

2 International Journal of Distributed Sensor Networks

D1

R

𝜌

S1

D4

D2

S2 D3S3

S4

Figure 1: Transmission interference model.

0

1 2 3

4 5 6

7 8 9

10 11 12

(a)

0

1 2 3

4 5 6

7 8 9

10 11 12

(9) (1)

(3)

(8)

(6)

(2)

(7)(4)(5)

(3)(2)

(1)

(b)

0

1 3

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7 9

10 12

2

5

11

8

(7) (6)(3)

(6) (2)

(5) (4)

(3)(1)(4)

(2)

(c)

Figure 2: Illustrations of single frequency channel.

2. Background

2.1. Transmission Interference Model. In wireless sensor net-works, each node has a given transmission radius 𝑅

𝑡and

an interference radius 𝜌. The communication range and theinterference range of a node V are illustrated by the twodisks centered at V of radius 𝑅

𝑡and radius 𝜌, respectively

(see node 𝑆1 in Figure 1). A pair of communication edges𝑆1 → 𝐷1 and 𝑆2 → 𝐷2 are said to be interference-free; if the two line segments (𝑆1, 𝐷2) and (𝑆2, 𝐷1) are bothlonger than 𝜌, they can be scheduled in the same time slot,as shown in Figure 1. Otherwise, they cannot be scheduledin the same time slot (e.g., 𝑆1 → 𝐷1 and 𝑆2 → 𝐷4). Weassume that a nodeworks in half-duplexmode, so it can eithersend or receive data at one time slot or it can receive datacorrectly only if exactly one of its neighbors is transmittingat that moment. For example, when 𝑆3 is transmitting to𝐷3,it cannot simultaneously receive the packet from 𝑆4.

2.2. Time Scheduling on a Single Frequency Channel. Anexample network is shown in Figure 2(a), and the dash linesamong nodes denote the communication neighborhood rela-tionship, where node 0 is sink node. A (Δ−1)𝑅 approximationalgorithm, Shortest Data Aggregation (SDA), is proposed byChen et al. [7], where Δ is the maximum degree and 𝑅 is theradius of the network. SDA constructs shortest spanning tree

(SPT) in the first phase. After that, the scheduling is iterativelyimplemented; each round introduces a schedule of the corre-sponding aggregation step. In round 𝑟, SDA picks sender onlyfrom the leaf nodes according to the interference-free princi-ple. The performance of SDA varies greatly, which dependson the SPT’s initial provision, and this is illustrated by theexample network in Figure 2(b) and 9 time slots are required.

GGT [8] algorithm is designed to construct the spanningtrees rooted at the sink, and the initial spanning tree containsonly the sink node. In each round, all nonleaf nodes of thecurrent spanning tree are the candidates of receivers, and allleaf nodes are the candidates of senders. As for the candidatesenders, there are two rules to sort them in a selectionsequence: (1) sort all nodes, based on the increasing order ofthe number of neighbors on the tree, and (2) sort nodes withthe same order by the first rule, based on the increasing orderof the number of neighbors out of the tree. The schedulingresult is shown in Figure 2(c) and 7 time slots are required.

2.3. Time Scheduling on Multiple Frequency Channels. Inthe transmission interference model [9], there exist twoconstraints: (1) adjacency constraint is due to the half-duplextransceiver on each node which prevents it from simul-taneous transmission and reception, as shown in Figure 1;𝑆3 → 𝐷3 and 𝑆4 → 𝑆3 cannot be scheduled in the same

International Journal of Distributed Sensor Networks 3

1 3

42

5 6

Sink

(a)

1 3

42

5 6

Sink

2, F2 3, F2

1, F2

1, F1

2, F1 3, F1

(b)

1 3

42

5 6

Sink

1, F1

2, F2

3, F3

2, F1

1, F2 3, F2

(c)

Figure 3: Illustrations of multiple frequency channels.

time slot as this constraint. (2) There is a wireless mediatransmission interference constraint. 𝑆1 → 𝐷1 and 𝑆2 →𝐷4 cannot be scheduled in the same time slot. Multichannelcommunication is an efficient method for eliminating thesecond constraint by enabling concurrent transmissions overdifferent frequencies.

In Figure 3(a), there is a network with 6 sensor nodesand the solid lines represent the tree edges, and the dashedlines represent the interfering links. JFTSS [10] schedules anetwork starting from the link that has the largest numberof packets (load) to be transmitted. When the load of theadjacent links is equal, such as in aggregated convergecast,the most constrained link is considered first, that is, the linkfor which the number of other links violating the interferingand adjacency constraints when scheduled simultaneouslyis the maximum. Figure 3(b) shows the aggregated tree,which is scheduled by JFTSS. In JFTSS, the link (2, sink) isfirstly assigned with frequency 𝐹1 and then the link (4, 1)is scheduled to frequency 𝐹2 in the first slot. It is hard tohave a distributed solution since the interference relationshipbetween all the links must be known.

TMCP [11] partitions the network into multiple subtreesand minimizes the intratree interference by assigning dif-ferent channels to the nodes residing on different branchesstarting from the top to the bottom of the tree. Figure 3(c)shows the same tree which is scheduled by TMCP to collectthe aggregated data. Here, the nodes on the leftmost branchare assigned with frequency 𝐹1, the nodes on the middlebranch are assigned with frequency 𝐹2, and the nodes onthe rightmost branch are assigned with frequency 𝐹3. Afterthe channel assignments, time slots are assigned to the nodesaccording to the BFS-Time Slot Assignment algorithm.

At present, many tree-based topology control and routingalgorithms are designed to aggregate and collect the sensingdata; these are appropriate for the small-scale, short commu-nication radius networks [12]. Multichannel communicationis an efficient method to eliminate interference by enablingconcurrent transmissions over different frequencies. But itis very difficult to assign channels to the tree networkstructure. Motivated by grid partition induction [13], wepropose AASA-GP to schedule the aggregation process. In

our algorithm, we firstly divide the network into grids basedon the geography information and then allocate channels tothe links based on grid coordinates. Nodes with the same gridcoordinate using the same channel, adjacent grids using theother channels, which can effectively avoid the transmissioninterference thereby reduce the aggregate delay. To the bestof our knowledge, it is the first time to use grid-based routingtopology to solve aggregation latency.

The following lists our key findings and contributions:

(1) Use the tree-based topology to route and solve aggre-gation latency.

(2) Allocate channel based on grid coordinates.(3) Algorithm is appropriate for large-scale wireless sen-

sor networks with the large communication range.

3. Protocol Description

3.1. Basic Idea. By dividing the network into grids andassigning different channels to adjacent grids, the wirelesstransmission medium interference constraint is avoided, andthe data from other source nodes in the same grid can becollected and aggregated on the selected cluster head and thenproceed to the sink.

3.2. Meshing. In our scheme, we randomly select 𝑁 wirelesssensor nodes to construct wireless sensor networks in 𝑆 ×𝑆 square region. Sink (deployed at the right side of thenetwork) broadcasts grid side length 𝑙 to the wireless sensornetworks, as shown in Figure 4; all nodes receive the messageaccording to the location information and the grid side lengthto calculate its grid coordinates:

𝐺𝑥 = ⌊𝑥

𝑙⌋ ,

𝐺𝑦 = ⌊𝑦

𝑙⌋ ,

(1)

where (𝐺𝑥, 𝐺𝑦) indicates the grid coordinates, (𝑥, 𝑦) indicatesthe location coordinates of the nodes, and ⌊𝑥/𝑙⌋ indicatesthe largest integer less than 𝑥/𝑙. The network is divided into


(0, 0) (1, 0) (2, 0) (3, 0)

(0, 1) (1, 1) (2, 1)

(0, 2) (1, 2)

(0, 3)Sink

lGy

Gx

K

...

4

3

2

1

0 1 2 3 4 · · ·

· · ·

· · ·

· · ·

· · · · · ·

K

S

Figure 4: Network mesh.

𝑚 = 𝑥2/𝑙2 grids, and the average number of nodes in each

grid is𝑁 ∗ 𝑙2/𝑥2.Each node broadcasts its grid coordinates, and the nodes

with the same grid coordinates will form a cluster, in whichthe highest-energy node serves as the cluster head andreceives the data from other members in this grid and thenaggregates the data into a fixed-size packet.

Due to the limitations of half-duplex mode, nodes withthe same grid coordinates cannot communicate with the clus-ter head at the same time, but nodes with the different gridcoordinates can communicate through multiple channels toavoid wireless media transmission interference and increasethe parallel transmission.

3.3. Channel Assignment. We assign different channels toadjacent grids, and the scheme of the channel assignmentof the network is shown in Figure 5, in which ch1 indicateschannel 1. According to this allocation, we assign 9 differentchannels to the entire network so that nodes in the differentgrid can transmit data at the same time. For example, inFigure 5, red grid is allocated channel 9 and its channelnumber is different from the adjacent grids. In this way, whennodes in the red grid communicate with cluster head, it isinterference-free with the adjacent 24 grids, in which reddashed line passes through. The total number of grids innetwork is 𝑥 ∗ 𝑥/𝑙 ∗ 𝑙, and the number of channels is 𝐹, sothe computational complexity of the channel assignment is𝑂(𝑥2∗ 𝐹/𝑙2).

At the same time, we can adjust the size of the grid(grid side length 𝑙) in order to guarantee nodes in red gridand in green grid to transmit data in parallel, so that nodesthat belong to different grids can transmit data withoutinterference. After the in-grid data collection, cluster headcan forward the sensed data across the other grids to sink.

ch1 ch2 ch3

ch4 ch5 ch6

ch7 ch8 ch9

ch1 ch2 ch3

ch4 ch5 ch6

ch7 ch8 ch9

ch1 ch2 ch3

ch4 ch5 ch6

ch7 ch8 ch9

ch1 ch2 ch3

ch4 ch5 ch6

ch7 ch8 ch9

ch1

ch1

Sink

ch9 ch9

Gy

K

... ...

...6

5

4

3

2

1

0 1 2 3 4 5 6 · · ·

· · ·

· · ·

· · ·

K Gx

Figure 5: Illustrations of channel assignment.

3.4. Routing between Grids. Routing across the grids mainlyinvolves the communication between cluster heads, and ourrouting scheme can be analyzed by following two casesaccording to the location of the sink.

In Figure 6, the example network is divided into a 8 ∗ 8grid. When sink locates at the center of the network, theroute scheme of this grid is shown as the directed arrows inFigure 6(a). The number of the same channels indicates thenumber of the time slots; the same number indicates data inthe two grids can be transmitted in parallel mode.

When sink is located in the center of the network, theroute structure between grids is shown in Figure 6(b).

3.5. The Connectivity of the Network. Because of the limita-tion of communication capabilities of wireless sensor nodes,we assume that communication radius is 𝑅

𝑡; the grid side

length is 𝐿. To obtain a better network connectivity, thecandidate cluster head must lie in the circular region whosecenter is the grid center and radius is 𝑅 as shown in Figure 7.

3.5.1. Connectivity within the Grid. As shown in Figure 7, wesuppose node A is the cluster head; if any node in the gridcould communicate with A, we should make the 𝐿

1satisfy

𝐿1≤ 𝑅𝑡; in other words, the following inequation should be

satisfied. Consider

𝑅 +√2

2𝐿 ≤ 𝑅

𝑡. (2)

3.5.2. Connectivity between the Grids. In order to guaranteethe adjacent cluster heads can communicate with each other,the maximum distance between two cluster heads should beless than the node communication radius 𝑅

𝑡. In Figure 8(a),


Sink

(1) (2) (3) (4)

(5)

(6)

(1) (2) (3)

(1) (2) (3)

(1) (2) (3)

(1) (2) (3)

(1) (2) (3)

(1) (2) (3)

(1) (2) (3)

(4)

(4)

(4)(7)

(8)(9)

(a) Sink is located at the center

Sink

(2)

(1)

(1)

(2)

(3)

(2)

(2)

(2)

(2)

(2)

(1)

(1)

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(4)

(3)

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(3)

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(5)

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(5)

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(6)

(6)

(7)

(8)

(9)

(10)

(b) Sink is located at the corner

Figure 6: Illustrations of data forwarding between grids.

B

A

L

R

L1

Figure 7: Cluster head selection area.

𝐿2≤ 𝑅𝑡(sink is in the center) or 𝐿

3≤ 𝑅𝑡(sink is in the

corner). That is,

2𝑅 + 𝐿 ≤ 𝑅𝑡, (3)

2𝑅 + √2𝐿 ≤ 𝑅𝑡. (4)

However, as shown in Figure 8(b), node G and node Huse the same channel 1; if they want to transmit the data inparallel mode, the grid side length 𝐿 should be satisfied as inthe following inequality:

2𝑅 ≤ 𝑅𝑡. (5)

When 𝐿 and 𝑅 are required to satisfy (3) or (4), they mustsatisfy (2).

In summary, when sink lies at the center or edge of thenetwork, if the network connectivity is to be ensured, 𝑅, 𝐿,and 𝑅

𝑡should satisfy the following constraints:

2𝑅 + 𝐿 ≤ 𝑅𝑡,

2𝐿 ≥ 𝑅𝑡.

(6)

When sink is in the corner of the network, 𝑅, 𝐿, and 𝑅𝑡

should satisfy the following constraints:

2𝑅 + √2𝐿 ≤ 𝑅𝑡,

2𝐿 ≥ 𝑅𝑡.

(7)

In (6) and (7), node’s communication radius 𝑅𝑡is a

constant, 𝐿 and 𝑅 are adjustable, and the greater the 𝐿 is, thesmaller the 𝑅 is. Thus the number of cluster heads to chooseis less; there may even be a grid that could not elect a clusterhead, so it should make 𝑅 as large as possible, so that therewill be plenty of nodes you can choose to be cluster headand cluster head’s energy consumption can be balanced. Forexample, when𝑅

𝑡= 30, (6) can take𝐿 = 15,𝑅 = 7.5, as shown

in Figure 8(c), and the nodes are located in the inscribedcircle of this grid. When sink is located at the center or edgeof the network, we make 𝐿 = 0.5𝑅

𝑡, 𝑅 = 0.25𝑅

𝑡. When sink

is located in the corner of the network, we make 𝐿 = 0.45𝑅𝑡,

𝑅 = 0.2𝑅𝑡.

3.6. Network Topology of the Algorithm. According to theabove algorithm description, we simulate a network in whichthe edge length is 200, the number of nodes is 800, thecommunication radius of node is 30, topology is shown inFigure 9, the red dots in each grid are cluster heads, the bluedot is sink, and the other dots are ordinary sensor nodes.


C D

E

F

L

L2

L3

R

(a)

G Hch1 ch2 ch3 ch1

L4

(b)

30

15

(c)

Figure 8: Connectivity between the grids.

Figure 9: Network topology.

4. Simulation and Performance Analysis

4.1. Experiment Setup. We use C++ to simulate the followingalgorithms. Multichannel algorithms are JFTSS-channel: 2 (2channels of JFTSS algorithm), JFTSS-channel: 16 (16 chan-nels of JFTSS algorithm), TMCP-channel: 2 (2 channels ofTMCP algorithm), TMCP-channel: 16 (16 channels of TMCPalgorithm), our algorithm (9 channels). Single-channel algo-rithms are SDA and GGT. The routing architecture of our

algorithm is based on grid, suitable for large-scale and largecommunication radius (𝑅

𝑡= 30, 40, 50) wireless sensor

networks. The topology structure of other algorithms ismainly based on the tree, and the node’s communicationradius of these algorithms is small (𝑅

𝑡= 10, 20, 30). Due

to differences in the application background, when ouralgorithm compared with other algorithms, we take 𝑅

𝑡= 30.

We randomly arrange 𝑁 sensor nodes in a square areawith the side length 𝑆; the average node density is𝑁/𝑆2. For arandomly generated network topology, we use average nodedegree Φ to indicate the strength of the interference. Here,The greater the average degree of nodes is, the stronger theinterference is.

4.2. Comparison with Other Algorithms. In our simulation,we set the average node density as 𝑁/𝑆2 = 0.02. For 𝑆 =50, 100, 150, 200, 250, we set 𝑁 = 50, 200, 450, 800, 1250,respectively. When the communication radius is set as 𝑅

𝑡=

10, 20, 30, 40, 50, the changes ofΦ are shown in Figure 10.With the increase of node communication radius, the

average degree of nodes also increases, so the networktransmission interference also increases; this results in theincrease of the aggregation delay.

Figure 11 shows the number of time slots neededwhen thenumber of nodes 𝑁 varies from 50 to 1250 (i.e., 𝑆 from 50


1020

3040

50

50100

150200

250

0

50

100

150

Transmis

sion rang

e

Square edge length

Aver

age d

egre

e

Figure 10: Average degree of the network.

to 250), with the 𝑅𝑡value of 10, 20, and 30. In Figure 11(a),

sink is located in the center of the network, the grid sidelength of AASA-GP is 𝐿 = 0.5, 𝑅

𝑡= 15, and the average

number of nodes in each grid is about 5. Due to the randomarrangement, the distribution of nodes in each grid is notuniform which lead to the AASA-GP aggregate delay in theactual simulation process that is higher than the theoreticalanalysis. As shown in Figure 11(a), AASA-GP reduces theaggregation delay by 20 percent compared to that by TMCP-16 channels and 40 percent compared to GGT.

In Figure 11(b), sink is located at the corner of thenetwork; the grid side length of AASA-GP is 𝐿 = 0.45,𝑅𝑡= 13.5. The aggregate delay of each algorithm has

increased to some extent; this is due to the increase of thedistance between sink and the other nodes. AASA-GP is stillsignificantly better than other algorithms; this reveals thatAASA-GP is applicable to the different topologies and has abetter performance in a wide range of applications.

4.3. Simulation of Large-Scale Wireless Sensor Networks. Wesimulate large-scale wireless sensor networks. 𝑆 varies from100 to 1000, with 𝑅

𝑡value of 30, 40, and 50, and the average

node density is set constant as 0.02. In Figure 12(a), sinkis located at the center of the network; when the networksize increases, the aggregation delay of AASA-GP increases.According to the three curves in Figure 12(a), we find that thetransmission interference increases when the node commu-nication radius increases; the transmission interference alsoincreases. But when the network size increases to a certainextent, the aggregate delay of 𝑅

𝑡= 40 and 𝑅

𝑡= 50 is

less than the aggregate delay of 𝑅𝑡= 30. This is due to the

fact that the larger the node communication radius is, thegreater the grid edge length is, which leads to the increasingof aggregate delay within the grid. However, at the same time,the number of grids decreases; the aggregate delay between

JFTSS, 2 channelsJFTSS, 16 channelsTMCP, 2 channelsTMCP, 16 channels

SDAGGTAASA-GP

0102030405060708090

100

Agg

rega

tion

time s

lots

0 100 150 200 250 30050Square edge length


JFTSS, 2 channelsJFTSS, 16 channelsTMCP, 2 channelsTMCP, 16 channels

SDAGGTAASA-GP

0102030405060708090

100

Agg

rega

tion

time s

lots

50 100 150 200 250 3000Square edge length


Figure 11: Performance comparison with fixed node density (𝑅𝑡=

30, Φ ≈ 40).

grids reduces. When the network size increases, this decreaseis more significant.

From Figure 12(b), we conclude that the variation trendof the aggregation network delay is similar to that shown inFigure 12(a), which indicates that AASA-GP can be appliedto different network topologies.

5. Conclusions

This paper presents an adaptive aggregation schedulingalgorithm based on the grid partition in large-scale wirelesssensor networks (AASA-GP). By dividing the network intogrids based on geographical information, when we assignthe different channels to the adjacent grids, the wirelesstransmission interference can be avoided. By selecting thecluster head in each grid, the network load can be effectivelybalanced. Simulation results show that aggregation delayby AASA-GP is significantly less than that by the otheralgorithms. In wireless sensor networks, when the networkscale and the node’s communication radius are larger, theadvantages of AASA-GP are more obvious.


200 300 400 500 600 700 800 900 1000100Square edge length

10

20

30

40

50

60

70

80

Agg

rega

tion

time s

lots

AASA-GP (Rt = 30)AASA-GP (Rt = 40)AASA-GP (Rt = 50)


200 300 400 500 600 700 800 900 1000100Square edge length

10

20

30

40

50

60

70

80

90

100

110

120

Agg

rega

tion

time s

lots

AASA-GP (Rt = 30)AASA-GP (Rt = 40)AASA-GP (Rt = 50)


Figure 12: Performance for large-scale wireless sensor networks.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

This work is partially supported by the Project of NationalNatural Science Foundation of China under Grant nos.71271165, 61373174 and 61572435, the Key Project of NaturalScience Foundation of Shaanxi Province under Grant nos.2015JZ002 and 2015JM6311, the Project of the Guangxi KeyLaboratory of Trusted Software under Grant no. kx201416,

the Project of the High Level Talents in Colleges of Guang-dong Province (Guangdong Finance Education (2013) no.246), and the Project of the Natural Science Foundation ofGuangdong Province under Grant no. 2014A030307014.

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