Fig 1.
Example of integer raster matrix (top), conceptual tree of the k2-raster (centre-top), conceptual tree using differential encoding (centre-bottom), and final representation of the raster matrix using compact data structures (bottom). rMax and rMin denote the maximum and minimum values of the root node. Lmax and Lmin contain the maximum and minimum values of each node, following a level-wise order and using differential encoding. This example uses k = 2.
Fig 2.
A vector dataset (left) and a raster dataset (right).
A vector dataset (left), and its MBRs, and a raster dataset (right), with the regions (quadrants) delimited by the divisions of the k2-raster. For clarity, the last level of the k2-raster is omitted.
Table 1.
Content of the stack during the example.
Table 2.
Content of the priority queue during the computation of a top-1 query over the example.
Table 3.
Raster dataset for Scenario I.
Values in Megabytes.
Table 4.
Raster dataset for Scenario II.
Values in Megabytes.
Fig 3.
Spatial distribution of the MBRs of the vector datasets vects (left) and vecca (right).
Fig 4.
Memory consumption (in Megabytes) for rasters in Scenario I.
(a) vects dataset and (b) vecca dataset.
Fig 5.
Memory consumption (in Megabytes) for rasters in Scenario II.
(a) vects dataset and (b) vecca dataset.
Fig 6.
Processing time (in seconds and log scale) with rasters of Scenario I.
(a) vects dataset and (b) vecca dataset.
Fig 7.
Processing time (in seconds and log scale) with rasters of Scenario II.
(a) vects dataset and (b) vecca dataset.
Fig 8.
Memory consumption vs processing time with the largest raster of Scenario I.
Memory consumption (in Megabytes) vs processing time (in seconds and log scale) with the largest raster of Scenario I. (a) vects dataset and (b) vecca dataset.
Fig 9.
Processing time (in seconds and log scale) with rasters of Scenario I and cold start.
(a) vects dataset and (b) vecca dataset.
Table 5.
Size of the datasets in Kilobytes.
Fig 10.
Processing time (in seconds) of the comparison with a classical data structure approach in Scenario I.
(a) vects dataset and (b) vecca dataset.
Fig 11.
Average memory consumption for retrieving the top-K over collections of Scenario I.
Average memory consumption (in Megabytes) for retrieving the top 1, 10 and 100 MBRs over collections of Scenario I. (a) top-1 and vects dataset, (b) top-1 and vecca dataset, (c) top-10 and vects dataset, (d) top-10 and vecca dataset, (e) top-100 and vects dataset and (f) top-100 and vecca dataset.
Fig 12.
Average memory consumption for retrieving the top-K over collections of Scenario II.
Average memory consumption (in Megabytes) for retrieving the top 10 MBRs over collections of Scenario II. (a) vects dataset and (b) vecca dataset.
Fig 13.
Average time results for retrieving the top-K over collections of Scenario I.
Average time results (in seconds) for retrieving the top 1, 10 and 100 MBRs over collections of Scenario I. We compare the results for all the algorithms using logarithmic scales for all the figures. (a) top-1 and vects dataset, (b) top-1 and vecca dataset, (c) top-10 and vects dataset, (d) top-10 and vecca dataset, (e) top-100 and vects dataset and (f) top-100 and vecca dataset.
Fig 14.
Time performance for retrieving the top-K MBRs over collections of Scenario II.
Time performance (in seconds) for retrieving the top 10 MBRs over collections of Scenario II. Both axes uses a logarithmic scale. (a) vects dataset and (b) vecca dataset.
Fig 15.
Box plots showing time results for retrieving the top-10 MBRs.
Box plots showing time results (in seconds) for retrieving the top-10 MBRs for the 25 matrices of collection DTM-1×1. The y axis is in logarithmic scale. (a) vects dataset and (b) vecca dataset.
Fig 16.
Memory consumption vs processing time with the largest raster of Scenario I and top-10.
Memory consumption (in Megabytes) vs processing time (in seconds) with the largest raster of Scenario I and top-10. (a) vects dataset and (b) vecca dataset.
Fig 17.
Time performance for retrieving the top-10 MBRs over collections of Scenario I in cold start.
The y axis uses a logarithmic scale. (a) vects dataset and (b) vecca dataset.