Indexing Spatio-Temporal Data Warehouses Dimitris Papadias, Yufei Tao, Panos Kalnis, Jun Zhang Department of Computer Science Hong Kong University of Science and Technology Clear Water Bay, Hong Kong 26, Feb, 2002 This work was supported by grants HKUST 6081/01E and 6070/00E from Hong Kong RGC.

2 Outline Preliminary – Spatial data warehouses and aggregate trees Applications and motivation Solution for static objects Solution for dynamic objects Performance study Conclusion

3 Preliminary – Spatial Data Warehouses Each spatial object carries some sort of aggregate information (i.e., each landscape may involve the population). A common query is the window aggregate query, which specifies a window query and retrieves the aggregate sum of all objects intersecting it. –Analogy of the “group-by” in conventional data warehouses. Materialization techniques common in traditional data warehouses are of limited use since possible positions of queries are infinite. –Ad-hoc “group-by” R1R1 R2R2 R3R3 R4R qsqs

4 Preliminaries – Spatial Data Warehouse A better approach is to deploy aggregate trees to introduce the spatial hierarchy [Kline and Snodgrass, 1995, Papadias, et al, 2001, Lazaridis and Mehrotra, 2001]. R1R1 R2R2 R3R3 R4R4 R5R5 R6R R1R1 150 R2R2 75 R3R3 132 R4R4 12 R5R5 225 R6R6 144 qsqs Aggregation R-tree Retrieve the sum of aggregate of objects intersecting q s

5 Spatio-Temporal DW: Applications and Motivation Spatio-temporal databases deal with objects whose properties may change with time. Traditional studies in spatio-temporal databases focus on retrieving the actual objects that satisfy the query predicates. –Retrieve all vehicles that appear in the north district during 3pm to 5pm yesterday. A more useful type of queries may be to retrieve, instead of the actual object IDs, the number of objects that satisfy the query conditions. –Retrieve the (approximate) number of vehicles in the north district during 3pm-5pm yesterday. In the above example, the spatial objects (i.e., streets in the north district) that carry aggregate information (i.e., number of cars) are static. Other queries may involve dynamic objects. –The mobile phone antenna (i.e., the aggregate information = # of users served by the antenna) whose spatial extents (i.e., covering areas) may change over time.

6 Example (Static Objects) Query q s retrieve the aggregate sum (during time T 1 -T 4 ) of all rectangles that intersect it.

7 Traditional Methods Pre-materialization –Even more difficult than spatial DW due to the inclusion of the temporal dimension. Use an aggregation tree. –When the aggregate of a region changes, create a 3D box. An aggregate 3D R-tree is used to index all these boxes. –Problem: The spatial extent of a region must be duplicated many times although it does not change. 3D boxes for region R T3T3 T4T4 T5T5 T1T1

8 Aggregate RB-tree Spatial extents are stored only once.

9 Example (Dynamic Objects) Query q s retrieve the aggregate sum (during time T 1 -T 4 ) of all rectangles that intersect it. R1R1 R2R2 R3R3 R4R4 qsqs Situation during timestamps 1-4

10 Example (cont.) Query q s retrieve the aggregate sum (during time T 1 -T 4 ) of all rectangles that intersect it. R1R1 R2R2 R3R3 R4R4 qsqs change position at timestamp 5

11 Aggregate HRB-tree Integrates the previous idea with the spatio-temporal access method HR-trees. timestamp 5 timestamp 1-4

12 Aggregate 3D RB-tree Creates a 3D box only when the spatial extent of an object changes.

13 Managing Numerous B-trees If each B-tree is too small (i.e., the rates of spatial extent and aggregate changes are similar) –A block contains too few entries and much space is wasted. –Not suitable for caching. Our solution is to use a B-File, which “packs” numerous B-trees into a single file –Avoiding empty spaces in a disk page. –Maintaining the same query performance.

14 Performance Dataset settings –Number of spatial objects = 10,000 –History length = 1,000 timestamps –Aggregate agility – describes how fast the aggregate information changes (4%, 8%, 16%, 32%, 64%) –Region agility – describes how fast the spatial extents change 0% for static objects 0.01% for dynamic objects (capturing the fact that spatial dimension changes much slower than the aggregate data) –Datasets include 500,000 to 6,500,5000 records. Each query contains 2 parameters: (spatial extents and interval length).

15 Results (Static Objects)

16 Results (Static Objects)

17 Results (Dynamic Objects)

18 Results (Dynamic Objects)

19 Conclusion We propose indexing techniques that replace the data cube in spatio- temporal data warehouses and answer ad-hoc group-by queries very efficiently. –Both static and dynamic spatial dimensions are discussed. Extensions –Cost models that predict the performance of alternative structures. –Query optimization based on the cost models. –Complex query evaluation