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International Journal of Distributed Sensor Networks
Volume 2012 (2012), Article ID 829253, 8 pages
http://dx.doi.org/10.1155/2012/829253
Research Article

A Novel Centroid Localization for Wireless Sensor Networks

Research Institute of Information Fusion, Naval Aeronautical and Astronautical University, Yantai 264001, China

Received 30 August 2011; Revised 14 November 2011; Accepted 23 November 2011

Academic Editor: Yingshu Li

Copyright © 2012 Yu Liu 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.

Abstract

Self-localization of sensor nodes is one of the key issues in wireless sensor networks. Based on the analysis of traditional range-free algorithms such as centroid and APIT (approximate perfect point in triangulation test) schemes, the effect of random deployment of all nodes on node localization is researched. And then, an improved centroid localization algorithm (ICLA) based on APIT and the quality of perpendicular bisector is proposed. In ICLA, nodes are categorized into several kinds and localized, respectively. Extensive simulation results indicate that ICLA obtains a better localization result in random topology networks without any additional hardware. Therefore, ICLA can be an alternate solution for the node self-localization problem in large-scale wireless sensor networks.

1. Introduction

The increasing miniaturization of electronic components and the advance in modern communication technology lead to the development of extreme small, cheap, and smart sensor nodes, which are able to sense the environment, compute simple tasks, and exchange data among each other. Interconnected assemblies of such devices, called Wireless Sensor Networks (WSNs), are commonly used to monitor huge inaccessible terrains [13].

The inherent characteristics of WSNs make a node’s location an important part of their state. For such networks, location is being used to identify the location at which sensor readings originate, which is essential in most of the WSNs applications [4], where the measurement data is meaningless without the knowledge of precise location from where it is obtained [5, 6]. In addition to the applications and protocols mentioned, continued research in WSNs will serve to invent and identify many additional protocols and applications, many of which will likely depend on location-aware sensing devices.

WSNs localization algorithms are used to estimate the location of sensor nodes in the network with knowledge of location of few specific nodes called beacon nodes, which can obtain their location using global positioning system (GPS), or by placement of beacon nodes at points with known coordinates.

Many localization algorithms have been proposed to provide location information of nodes. With regard to the mechanisms used for estimating location, these localization protocols are classified as two categories: range-based methods [7, 8] and range-free methods [9, 10]. The former is defined by protocols that use absolute point-to-point distance estimates (range) or angle estimates for calculating location. The latter makes no assumption about the availability or validity of such information. Because of the hardware limitations of WSNs devices, solutions in range-free localization are being pursued as a cost-effective alternative to more expensive range-based approaches.

Bulusu et al. proposed a simple range-free localization algorithm called Centroid Localization Algorithm (CLA), which needs only a minimum of computations [9]. In CLA, all nonlocalized nodes calculate their position as the centroid of all received beacon’s positions. But the inherent bias of CLA was not considered. In Recent years, some improved Centroid algorithms based on certain weighted methods have been proposed. Most of the improved algorithms have combined the distance information and require distance measurement through some range methods like Received Signal Strength Indicator (RSSI), which depress the expansibility. What’s more, the localization of nodes on the edge of network has not been considered in most range-free algorithms. With special topology, these nodes should be treated distinguishingly. Or else, the average localization accuracy will be affected negatively.

In this paper, without using RSSI or any other parameter, we present our investigations concerning the bias of CLA and the achievable improvement when correcting the bias, utilizing APIT (approximate perfect point in triangulation test) [10] and the quality of perpendicular bisector. Our approach (ICLA) will be evaluated in terms of accuracy and communication overhead, compared with CLA. Moreover, we extend our approach to localize nodes at the borders of the network to improve average localization accuracy.

The remainder of the paper is organized as follows. In Section 2, the original CLA algorithm is introduced and analyzed. In Section 3, our approach (ICLA) to reduce the localization bias of centroid estimation is proposed. In Section 4, results of the corresponding computer simulations are presented and the performance of ICLA is compared with CLA. Finally, Section 5 closes with a conclusion and future work.

2. State of the Art

The only kind of distance information used in CLA is the binary information whether the unknown is in the communication range of a beacon or not. CLA acts from the assumption which that each beacon has a circular area within it can communicate with other nodes. In Figure 1, it is shown how the communication ranges of four beacons, arranged as described above, build up to several intersecting areas within an unknown can be localized.

829253.fig.001
Figure 1: Localization principle of CLA.

CLA uses the location information of all beacons in range to calculate the position as the centroid of the received beacon positions [9], as the centroid as shown in (1). In this formula, 𝑈𝑖(𝑥,𝑦) indicates the position of unknown 𝑖 given by its two-dimensional coordinates. The known position of beacon 𝑗 is given by 𝐵𝑗(𝑥,𝑦). The number of beacons which are within the communication range of the unknown node is indicated by 𝑚𝑈𝑖1(𝑥,𝑦)=𝑚𝑚𝑗=1𝐵𝑗(𝑥,𝑦).(1)

Depending on the given calculation, a node which is situated within one of the intersecting areas will calculate its position at one single point, regardless of its exact position within the intersection area. For example, a node which is able to communicate to all of the four beacons will calculate its position in the centre of the arrangement, as shown in Figure 1.

This behavior leads to a relative high localization failure, given as the Euclidian distance between the exact position of a sensor node and its calculated position. Blumenthal et al. showed in [11] that the averaged localization failure cannot be less than 18% of the beacon distance for CLA. This comes along with a maximum localization failure of 45%. This corresponds with the findings published by Bulusu et al. in [9]. Blumenthal et al. also showed that the localization failure depends on the ratio between the beacon distance and the communication range. The cited values belong to an optimal transmission range of 87% of the beacon distance as it is illustrated in Figure 1.

However, former analysis of CLA mostly investigated the impact of the transmission range on the accuracy of the localization [12, 13], and some simulation were carried out in a 4-beacon scenario [11, 14, 15] which can be impractical for large-scale outdoor sensor network.

3. Improved Centroid Localization Algorithm

To reduce the localization bias in asymmetry network, an improved centroid estimation method based on APIT and the quality of perpendicular bisector is proposed in this section.

3.1. Analysis of Different Nodes in Network

Obviously, the location of beacon nodes impacts the estimated centroid, as a result, it also affects the localization error. It is instinctive that any three different beacon nodes not in a line can form different triangle. And approximate perfect point in triangulation test (APIT), which takes advantage of the relatively high node density of these networks and uses neighbor information exchanged via beaconing to emulate the node movement, can judge which triangles an unknown node resides in [10]. For a detailed analysis of network topology, according to the distribution of beacon nodes in transmission range and results of APIT, unknown nodes in network can be classified as four categories: normal node, side node, hypoisolated node, and isolated node. Suppose nrb𝑖 denotes the number of beacon nodes around node 𝑖 (within transmission range) and inTr𝑖 represents the number of triangles where node 𝑖 resides in, then(1)node 𝑖 is defined as a normal node when nrb𝑖3 and inTr𝑖>0;(2)node 𝑖 is defined as a side node when nrb𝑖3 and inTr𝑖=0;(3)node 𝑖 is defined as a hypo-isolated node when nrb𝑖=1 or nrb𝑖=2;(4)node 𝑖 is defined as an isolated node when nrb𝑖=0.

In order to study the node distribution of different categories in random network, MATLAB is adopted in the following simulation experiments. We assume that 200 sensor nodes (50 beacon nodes and 150 unknown nodes, with the same transmission range) are deployed randomly in a square field of 100 m × 100 m, and the transmission range of each node is 20 meters. Figure 2 shows nodes distribution in a virtual simulation and Figure 3 indicates the percentage of different categories of nodes to all unknown nodes versus transmission range.

829253.fig.002
Figure 2: Nodes distribution.
829253.fig.003
Figure 3: Percentage of different categories of nodes to all unknown nodes versus transmission range.
3.2. Analyzes of Normal Node

Node 𝑖 is a normal node, which means that Node 𝑖 resides in at least one triangle formed by beacon nodes. And the location problem of node 𝑖 can be solved by an improved CLA based on APIT and the quality of perpendicular bisector, as showed in Figure 4. These triangles formed by beacon nodes are picked out to estimate the location of the unknown node, that is, according to the property of the three altitudes, a triangle can be divided into some small cells. One of these cells, which the unknown node resided in, can be estimated out, utilizing received signal strength (RSS) value between the three beacon nodes and the unknown node for the reason that RSS reflects the distance between two nodes in transmission range.

829253.fig.004
Figure 4: Illustration of ICLA in an acute triangle.

Suppose a line which passes through two points 𝐵𝑖(𝑥𝑖,𝑦𝑖) and 𝐵𝑗(𝑥𝑗,𝑦𝑗), then the equation of perpendicular bisector of the line can be depicted as follows:𝑥𝑦=𝑖𝑥𝑗𝑥𝑥𝑖+𝑥𝑗/2𝑦𝑗𝑦𝑖+𝑦𝑖+𝑦𝑗2.(2)

If unknown node resides in a triangle, without loss of generality (WLOG), for an acute triangle Δ𝐵1𝐵2𝐵3, three perpendicular bisectors meet the three edges of Δ𝐵1𝐵2𝐵3 at six feet and divide Δ𝐵1𝐵2𝐵3 into six small cells, as showed in Figure 4. Then, unknown node assigns itself to a cell by RSS from the beacons (three vertices of triangle Δ𝐵1𝐵2𝐵3). Finally, the node localizes itself at the estimated centroid of the according cell.

WLOG, suppose an unknown node 𝑈𝑖 resides in Δ𝐵1𝐵2𝐵3 and 𝑆𝑆𝑖𝑗 denotes the received signal strength of node 𝑖 from node 𝑗. Obviously, if 𝑆𝑆𝑖1>𝑆𝑆𝑖2>𝑆𝑆𝑖3, we can conclude that 𝑈𝑖 resides in the small cell (1), as showed in Figure 4. Then, besides 𝐵1, the location problem of the other three vertices of the quadrangle 𝐵1𝐵12𝑂𝐹13 can be solved by equations as follows: 𝑦𝑜=𝑥1𝑥2𝑥𝑜𝑥1+𝑥1/2𝑦2𝑦1+𝑦1+𝑦22,𝑦𝑜=𝑥1𝑥3𝑥𝑜𝑥1+𝑥3/2𝑦3𝑦1+𝑦1+𝑦32,𝑦𝑓13=𝑦3𝑦1𝑥3𝑥1𝑥𝑓13𝑥1+𝑦1,𝑦𝑓13=𝑥1𝑥3𝑥𝑓13𝑥1+𝑥3/2𝑦3𝑦1+𝑦1+𝑦32,𝑦𝐵12=𝑦2𝑦1𝑥2𝑥1𝑥𝐵12𝑥1+𝑦1,𝑦𝐵12=𝑥2𝑥3𝑥𝐵12𝑥2+𝑥3/2𝑦3𝑦2+𝑦2+𝑦32,(3) where 𝑂(𝑥𝑜,𝑦𝑜) denotes the circumcenter of triangle Δ𝐵1𝐵2𝐵3, the perpendicular bisector of line 𝐵1𝐵3 meets 𝐵1𝐵3 at 𝐹13(𝑥𝑓13,𝑦𝑓13) and the perpendicular bisector of line 𝐵2𝐵3 meets 𝐵1𝐵2 at 𝐵12(𝑥𝐵12,𝑦𝐵12). However, 𝑂, 𝐹13, and 𝐵12 become three pseudo beacons which can be used to localize the unknown node 𝑈𝑖. Finally, node 𝑈𝑖 localizes itself at the estimated centroid of the quadrangle 𝐵1𝐵12𝑂𝐹13. Then, if a node resides in 𝑛 triangles and each triangle can get an estimated centroid, the node can localize itself at the average location of these 𝑛 centroids.

Besides, right triangle and obtuse triangle can be divided into four cells by three perpendicular bisectors, as showed in Figure 5.

fig5
Figure 5: Triangle divided by Perpendicular Bisectors: (a) right triangle; (b) obtuse triangle.
3.3. Analyzes of Side Node

If nrb𝑖3 and inTr𝑖=0, it means that beacon nodes are deployed on one side of unknown node 𝑈𝑖. Actually, if unknown nodes are deployed closely to network edge or beacon nodes are not enough, there will always be some side nodes in network, as showed in Figure 3. However, this problem has been noticed by few publicized algorithms based on CLA. And if side nodes localize themselves using CLA, it is intuitive that this centroid estimate will contribute to large localization error, as showed in Figure 6. Besides, the large localization bias of side nodes will directly affect the network average localization accuracy. Fortunately, this problem is specially analyzed in ICLA. Then, a feasible and simple scheme is proposed for side node localization.

829253.fig.006
Figure 6: Localization principle of side node in ICLA.

Obviously, range between nodes is in inverse proportion to RSS. In the environment with no signal disturbance, feebler RSS indicates farther range. Thus, in a densely deployed network, the range corresponding to the feeblest RSS inclines to the transmission range (𝑅). According to this relation, beacon nodes around unknown node 𝑈𝑖 can be arranged in the corresponding RSS. Then, the two farther beacon nodes 𝐵1(𝑥1,𝑦1) and 𝐵2(𝑥2,𝑦2) away from 𝑈𝑖 are selected as reference nodes and the nearest beacon node 𝐵3(𝑥3,𝑦3) as a verifier, as showed in (4). Concretely, suppose the distance between reference node and 𝑈𝑖 to be 𝑅, then get two estimated location 𝑈𝑡 and 𝑈𝑓, among which 𝑈𝑓 is verified as the incorrect one by the distance away verifier. In other words, the location problem of 𝑈𝑖(𝑥𝑒,𝑦𝑒) can be solved by 𝑥min𝑒𝑥32+𝑦𝑒𝑦32,𝑥𝑒𝑥12+𝑦𝑒𝑦12=𝑅,𝑥𝑒𝑥22+𝑦𝑒𝑦22=𝑅.(4)

3.4. Analyzes of Hypoisolated Node

For hypoisolated nodes, CLA still performs only averaging the coordinates of beacon devices to localize blindfolded devices. However, ICLA uses weights to ensure an improved localization. Starting from the calculation of the arithmetic centroid as showed in (1), the formula to determine the position with Weighted CLA is derived. Expressing the term 𝑚 as sum of ones and the multiplication of 𝐵𝑗 with ones, (1) is expanded to 𝑈𝑖(𝑥,𝑦)=𝑛𝑗=11𝐵𝑗(𝑥,𝑦)𝑛𝑗=11.(5)

After replacing ones in (5) by weight functions 𝑤𝑖𝑗, the final equation is formed as follows:𝑈𝑖(𝑥,𝑦)=𝑛𝑗=1𝑤𝑖𝑗𝐵𝑗(𝑥,𝑦)𝑛𝑗=1𝑤𝑖𝑗.(6)

The weight 𝑤𝑖𝑗 is a function depending on the RSS, which indicates distance between beacon dispatcher and receiver. Every application scenario requires a different weight due to changed environment conditions. Of course, shorter distances are more weighted than higher distances and 𝑤𝑖𝑗 and 𝑑𝑖𝑗 are inversely proportional. But 𝑑𝑖𝑗 is difficult to acquire, or need additional hardware which will contribute to more energy spending. However, RSS𝑖𝑗 and 𝑑𝑖𝑗 are also inversely proportional. Thus, in ICLA, for a concentric wave expansion with a linear characteristic of the receiver and a uniform density of the beacons, we form 𝑤𝑖𝑗=RSS𝑖𝑗.(7)

3.5. A Walk through ICLA

In this section, we present an example to further explain our localization scheme ICLA.(1)In the first phase, all beacon nodes send their position 𝐵𝑗(𝑥,𝑦) to all sensor nodes within their transmission range.(2)Suppose that an unknown node 𝑀 has received 𝑛 beacons. 𝑛=0 indicates that 𝑀 is an isolated node and 1𝑛2 indicates that 𝑀 is a hypoisolated node which can be localized using the algorithm described in Section 3.4. However, if 𝑛3, 𝑀 is a normal node or side node.(3)Each node maintains a data table (beacon node ID, Location, RSS) for each beacon node heard, that is, node 𝑀 has received beacons from beacon nodes 𝐴, 𝐵, 𝐶, 𝐷 and as showed in Table 1 and node 1 in Table 2.(4)Then, each node beacons once to exchange data tables with its neighbors. Thus, these data tables are merged at every node to maintain neighbors state. Suppose node 𝑖 to be neighbor of node 𝑀, 1𝑖𝑚. Combined data of node 𝑀 is showed in Table 3.(5)Beacon nodes 𝐴, 𝐵, 𝐶, and 𝐷 can form four triangles Δ𝐴𝐵𝐶, Δ𝐴𝐵𝐷, Δ𝐴𝐶𝐷, and Δ𝐵𝐶𝐷. For each triangle, APIT runs on every column of the node’s table to determine whether a neighboring node exists that has consistently larger or smaller signal strengths from any three beacon nodes. If such a neighbor is found, 𝑀 assumes that it is outside this triangle. Otherwise, if no such neighbor is found, 𝑀 assumes it is inside this region.(6)Like node 𝑀, each node repeats step (5) for varying combinations of three beacon nodes. Then, if node 𝑀 does not reside in any triangle, it is a side node which can be localized using the algorithm described in Section 3.3.(7)And if node 𝑀 resides in 𝑟(𝑟1) triangles which means 𝑀 is a normal node, the algorithm described in Section 3.2 is then used to determine the final location estimation of 𝑀.

tab1
Table 1: Node 𝑀.
tab2
Table 2: Node 1.
tab3
Table 3: Combined data of node 𝑀.

4. Performance Evaluation

This section provides a detailed quantitative analysis evaluating the performance of ICLA compared with CLA.

4.1. A Note in Evaluation

The obvious metric for comparison when evaluating localization schemes is localization error. We have conducted a variety of experiments to cover a wide range of system configurations including varying (1) percentage of beacon node (PBN), (2) transmission range (𝑅), (3) radio propagation patterns denoted by degree of irregularity (DOI) and (4) success rate of APIT (SRA), a common set of system parameters shared by most range-free localization algorithms.

However, it is better to note that since there is no interaction between nodes in the ICLA, instead, we take SRA as a system parameter to evaluate algorithm. On the other hand, because communication can have a significant impact on wireless sensor network systems, communication overhead in terms of number of messages exchanged, as a telling secondary metric, is used to evaluate the cost and performance of ICLA.

We assume that 200 nodes, including beacon nodes and unknown nodes, are deployed randomly in a square field of 100 m × 100 m. Outside of studying the effect of certain parameters on localization error, we use default values of PBN = 30%, 𝑅=30 m, DOI = 0.1, and SRA = 0.9 in most of our experiments. These settings are in line with our expectation of future sensor network technology and facilitate comparisons between figures. And in all of our graphs, each data point represents the average value of 100 trials with different random seeds.

4.2. Localization Error When Varying PBN

In this experiment, we analyze the effect of varying percentage of beacon node (PBN) in network to determine its effect on localization error for random node placement. Figure 7 shows that the overall estimation error constantly decreases as PBN increases. We note that CLA and ICLA are both sensitive to PBN due to the fact that centroid estimation in these two schemes similarly relies on the average data of beacons around. However, it is important to note that our ICLA algorithm consistently performs better than the CLA and ICLA requires only less than 25% PBN to reach the 0.15R level while the CLA requires more than 45%. This is due to the fact that the possible area where unknown node resides in is much smaller. And this effect is significantly enlarged by increasing PBN.

829253.fig.007
Figure 7: Localization error under varying PBN. 𝑅=30 m, DOI = 0.1, SRA = 0.9.
4.3. Localization Error When Varying 𝑅

Figure 8 explores the effect of transmission range (𝑅) on the localization estimation accuracy. Because the number of beacon nodes heard is affected by transmission range, the estimation error is large when 𝑅 is below 20 m. But it should be noted that localization error decreases consistently and rapidly as 𝑅 increases for ICLA but not for CLA, due to larger accumulated error result from larger beacon propagation distances and its relatively simple design in CLA.

829253.fig.008
Figure 8: Localization error under Varying 𝑅. PBN = 0.3, DOI = 0.1, SRA = 0.9.

And in comparison to CLA, the increase in the location accuracy for ICLA is due to the fact that an increase in the transmission range results in more triangles formed by beacon nodes taking part in localization. Especially, ICLA can produce good results (localization error below 15%) as long as transmission range remains above 30 m.

4.4. Localization Error When Varying DOI

Simulation in Almost all algorithms assumes that radio patterns are perfectly circular, which disaccords with wireless communication. And it is intuitive that irregular radio patterns can affect the network topologies resulting in irregular node connectivity. So, in this experiment, the impact of irregular radio patterns on the precision of localization estimation is investigated.

We can see, in Figure 9, how the inaccurate estimate directly contributes to localization error as the DOI increases. In the same way, CLA and ICLA acquire beaconed information using online information exchanged between beacon nodes. However, because the effect of DOI is abated by the aggregation of beaconed information and localization results in different combinations of beacon nodes are fused in ICLA, ICLA is more robust than CLA relatively.

829253.fig.009
Figure 9: Localization error under varying DOI. PBN = 0.3, 𝑅=30 m, SRA = 0.9.
4.5. Localization Error When Varying SRA

Because APIT can only evaluate a finite number of directions (the number of neighbors), APIT can make an incorrect decision (InToOut error and OutToIn error). Fortunately, from experimentation, He et al. find that the percentage of APIT tests exhibiting such an error is relatively small (14% in the worst case). When node density increases, APIT can evaluate more directions, considerably reducing OutToIn error. On the other hand, InToOut error will slightly increase due to the increased chance of edge effects. Figure 10 shows the effect of SRA on the localization estimation accuracy. We note that the overall localization error constantly decreases as SRA increases. This occurs because APIT is a key phase, which determines how much beacon triangles used in node localization and which category the unknown node belongs to. It is instinctive that more authentic data for localization leads to more accurate results. However, we also note that when the SRA is higher than 0.9, localization error toboggans (under 0.2R) due to the increase of available data for localization. In this system configuration, ICLA has good performance.

829253.fig.0010
Figure 10: Localization error under varying SRA. PBN = 0.3, DOI = 0.1, 𝑅=30 m.
4.6. Evaluation Summary

In addition to the analysis previously described, a variety of experiments have been conducted to cover a varying range of system configurations for evaluating localization schemes in this section. These experiments help us better understand the situations where our localization scheme considered is more appropriate than CLA.

From our extensive comparison study, we identify preferable system configurations of traditional range-free localization schemes as a design guideline for further research. In particular, an ICLA scheme, proposed in this paper, performs better than CLA when percentage of beacon node, irregular radio patterns, and random node placement are considered. Moreover, we provide insight on how the transmission range and success rate of APIT affect the localization error. These results show that the accuracy provided by ICLA is sufficient to support various WSNs applications mainly discussed in [10]. However, ICLA requires more communication overhead than the CLA because of the neighborhood information exchange for APIT. In great detail, CLA requires that only each beacon node beacons once, but each beacon node or unknown node in network has to beacon once in ICLA. Nevertheless, communication overhead in ICLA, as much as APIT scheme, increases with increased node density; however, it does so at a much lower rate than some localization algorithms using flood-style transmission [10].

On the other hand, we can conclude that aggregated decisions can provide good accuracy during location estimation by exploiting redundancy and high node density, which are the key positive characteristics of wireless sensor networks over traditional ad hoc networks, regardless of the fact that information obtained by an individual test is coarse and error-prone.

5. Conclusion and Outlook

Given the inherent constrains of the sensor devices envisioned and the estimation accuracy desired by location-dependent applications, range-free localization schemes are regarded as a cost-effective and sufficient solution for node self-localization in sensor networks.

A simple approach for coarse grained localization is centroid localization algorithm (CLA) which assumes regularly arranged beacons. Unfortunately, CLA has a biased error, especially when all sensor nodes are deployed randomly. Based on investigation of the bias and its impacts on localization error, this paper presented ICLA as an improvement of CLA. ICLA approach achieves considerable improvements in accuracy by utilizing additional topological knowledge and RSS. And we showed that correcting the location estimating of normal nodes as well as side nodes and hypoisolated node leads to improved accuracy. The correction for side nodes is from special significance. These nodes, usually being deployed at the edges of the sensor field and not enclosed by beacons communication ranges, need special localization scheme presented in ICLA.

In conclusion, our approaches to correct localization error in this paper are also of practical importance and can be used for irregularly arranged networks with relatively large number of beacons. Future research may include an adaptation of other CLA-based localization algorithms. In addition, a number of practical factors which may affect efficiency, accuracy, and flexibility of our localization approaches will also be considered.

Acknowledgment

This work was financially supported by Shandong Provincail Natural Science Foundation of China under Grant no. ZR2011FQ002.

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