Optimizing Multi-Way Spatial Joins of Web Feature Services
Abstract
:1. Introduction
2. Multi-Way SPATIAL Join of Web Feature Services
2.1. Open Geospatial Consortium (OGC) Web Feature Service
2.2. Multi-Way Spatial Join
2.3. Issues in Spatial Join Processing of Multiple Web Feature Services (WFSs)
3. The Optimization Algorithm for a Multi-Way Spatial Join of WFSs
3.1. Optimizing Binary Spatial Join of Web Feature Services
- (1)
- Merge the white and diagonal sub-areas into a larger area, and send its boundary to Server A to download R1 objects contained in or crossing this boundary. Merge the black and diagonal sub-areas into a larger area, and send its boundary to Server B to download R2 objects contained in or crossing this boundary.
- (2)
- For the white sub-areas, a spatial semi-join is performed on Server B, and the candidate objects of the dataset R2 are sent to the client. For the black sub-areas, a spatial semi-join is performed on Server A and the candidate objects of the dataset R1 are sent to the client.
- (3)
- The immediate datasets are refined on the client side to obtain the final solutions of the spatial join.
3.2. Optimizing the Multi-Way Spatial Joins of Web Feature Services
- (1)
- Estimate the filtering rates for all of the binary joins in the query graph with Equation (2).
- (2)
- Perform the join with the highest priority (usually determined by the filtering rate). After that, recalculate the filtering rate of the other binary joins with respect to the above two joined datasets, if necessary.
- (3)
- Repeatedly perform step (2) until all of the candidate objects of the related datasets have been downloaded to the client site.
Algorithm 1: Processing multi-way spatial joins |
Multiway-SpatialJoin(Datasets){ Foreach (Relation(i, j) in RelationSets) { /*Compute filtering rates for every binary join */ S(i, j)=ComputeFilteringRate (Datasets[i], Datasets[j]); } While (RelationSets ≠∅){ /*Stop if RelationSets is empty*/ Find the binary join with them maximum filtering rate S(n, m) or the Relation(n, m) that both datasets have a very small number of features; SpatialJoin(Datasets[n], Datasets[m]); /*Join Datasets[n] and Datasets[m]*/ Update(Datasets[n], Datasets[m]); /* Substitute Datasets[n] and Datasets[m] with the immediate solution of the previous join*/ Remove( Relation(n, m) ); /*Remove Relation(n, m) from RelationSets */ Update the filtering rates of the other joins that Datasets[n] and Datasets[m] participate in; } } |
4. Experiment Analysis
4.1. Test of Binary Spatial Join
4.2. Test of Multi-Way Spatial Join
4.3. Test with Different Connection Speeds
5. Discussion
Acknowledgments
Author Contributions
Conflicts of Interest
References
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No. | DS_SHF (MB) | DS_XML (KB) | ENCODE_T (s) | PARSE_T (s) | TRANS_T (s) | TOTAL (s) |
---|---|---|---|---|---|---|
1 | 1 | 2472 | 0.82 | 1.14 | 0.66 | 2.62 |
2 | 3 | 7476 | 2.44 | 3.69 | 1.37 | 7.5 |
3 | 5 | 12,932 | 4.42 | 6.23 | 2.56 | 13.21 |
4 | 7 | 17,835 | 5.95 | 8.76 | 4.08 | 18.79 |
5 | 9 | 22,902 | 7.54 | 11.07 | 5.43 | 24.04 |
6 | 11 | 28,343 | 9.3 | 13.75 | 6.88 | 29.93 |
7 | 13 | 33,749 | 13.08 | 17.79 | 9.1 | 39.97 |
8 | 15 | 38,293 | 15.1 | 19.92 | 11.07 | 46.09 |
9 | 17 | 44,420 | 17 | 23.75 | 12.32 | 53.07 |
10 | 19 | 49,157 | 20.03 | 26.87 | 13.53 | 60.43 |
T = 30 | T = 50 | T = 100 | Average | |
---|---|---|---|---|
X ≥ 1.5 | 45.0% | 60.0% | 42.0% | 49.0% |
1.5 > X > 1.0 | 32.0% | 20.0% | 35.0% | 29.0% |
X ≤ 1.0 | 23.0% | 20.0% | 23.0% | 22.0% |
T = 30 | T = 50 | T = 100 | Average | |
---|---|---|---|---|
X ≥ 1.5 | 53.0% | 70.0% | 51.0% | 58.0% |
1.5 > X >1.0 | 24.0% | 8.0% | 26.0% | 19.3% |
X ≤ 1.0 | 23.0% | 22.0% | 23.0% | 22.7% |
Dataset Name | Geometric Type | Number of Objects | Data Size (kb) |
---|---|---|---|
primary roads | polyline | 12,101 | 40,061 |
uac10 | polygon | 3976 | 108,422 |
place | polygon | 29,130 | 167,240 |
rails | polyline | 180,739 | 64,872 |
school | polygon | 6846 | 171,507 |
Types | Number of Objects | Notably Improved | Slightly Improved | Futile | |||
---|---|---|---|---|---|---|---|
M1 | M2 | M1 | M2 | M1 | M2 | ||
Three-way | [54,1349] | 7 | 3 | 54 | 47 | 14 | 25 |
Four-way | [196,4131] | 18 | 0 | 48 | 59 | 9 | 16 |
Five-way | [234,4271] | 20 | 1 | 50 | 69 | 5 | 5 |
Speed | Unlimited | 4 Mbps | 2 Mbps | 1 Mbps | 0.5 Mbps | |||||
---|---|---|---|---|---|---|---|---|---|---|
NO. | M1 | M3 | M1 | M3 | M1 | M3 | M1 | M3 | M1 | M3 |
1 | 13.02 | 14.86 | 13.39 | 15.56 | 13.37 | 17.42 | 14.23 | 20.84 | 19.72 | 31.37 |
1 | 17.12 | 22.12 | 19.86 | 28.52 | 24.39 | 36.89 | 32.37 | 48.74 | 45.98 | 71.24 |
2 | 22.45 | 31.32 | 29.07 | 44.08 | 45.58 | 65.19 | 72.03 | 102.02 | 94.74 | 138.92 |
3 | 24.66 | 30.75 | 32.64 | 43.75 | 48.15 | 61.74 | 61.64 | 78.82 | 85.14 | 118.32 |
4 | 42.97 | 53.59 | 50.06 | 67.02 | 63.53 | 87.08 | 90.84 | 138.07 | 158.08 | 239.42 |
5 | 33.05 | 49.61 | 41.49 | 62.52 | 54.23 | 83.92 | 78.48 | 124.71 | 117.97 | 188.49 |
6 | 30.65 | 38.12 | 45.76 | 58.62 | 65.62 | 85.57 | 90.27 | 128.3 | 147.02 | 210.15 |
7 | 31.06 | 43.93 | 45.6 | 62.98 | 57.74 | 80.67 | 74.86 | 107.37 | 104.72 | 150.37 |
8 | 20.16 | 27.11 | 23.54 | 33.25 | 30.38 | 45.06 | 42.56 | 61.68 | 60.92 | 93.35 |
9 | 12.19 | 12.48 | 12.97 | 13.8 | 15.17 | 15.88 | 17.51 | 18.4 | 20.22 | 22.4 |
10 | 16.87 | 18.67 | 16.68 | 21.22 | 19.6 | 25.91 | 23.05 | 31.49 | 30.36 | 41.05 |
11 | 26.19 | 35.49 | 40.44 | 56.27 | 50.74 | 78.84 | 82.53 | 117.6 | 118.63 | 170.3 |
No. | Unlimited | 4 Mbps | 2 Mbps | 1 Mbps | 0.5 Mbps |
---|---|---|---|---|---|
1 | 1.14 | 1.16 | 1.30 | 1.46 | 1.59 |
2 | 1.29 | 1.44 | 1.51 | 1.51 | 1.55 |
3 | 1.40 | 1.52 | 1.43 | 1.42 | 1.47 |
4 | 1.25 | 1.34 | 1.28 | 1.28 | 1.39 |
5 | 1.25 | 1.34 | 1.37 | 1.52 | 1.51 |
6 | 1.50 | 1.51 | 1.55 | 1.59 | 1.60 |
7 | 1.24 | 1.28 | 1.30 | 1.42 | 1.43 |
8 | 1.41 | 1.38 | 1.40 | 1.43 | 1.44 |
9 | 1.34 | 1.41 | 1.48 | 1.45 | 1.53 |
10 | 1.02 | 1.06 | 1.05 | 1.05 | 1.11 |
11 | 1.11 | 1.27 | 1.32 | 1.37 | 1.35 |
12 | 1.36 | 1.39 | 1.55 | 1.42 | 1.44 |
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Lan, G.; Zhang, Q.; Yang, Z.; Li, T. Optimizing Multi-Way Spatial Joins of Web Feature Services. ISPRS Int. J. Geo-Inf. 2017, 6, 123. https://doi.org/10.3390/ijgi6040123
Lan G, Zhang Q, Yang Z, Li T. Optimizing Multi-Way Spatial Joins of Web Feature Services. ISPRS International Journal of Geo-Information. 2017; 6(4):123. https://doi.org/10.3390/ijgi6040123
Chicago/Turabian StyleLan, Guiwen, Qiang Zhang, Zhao Yang, and Tong Li. 2017. "Optimizing Multi-Way Spatial Joins of Web Feature Services" ISPRS International Journal of Geo-Information 6, no. 4: 123. https://doi.org/10.3390/ijgi6040123