1. Querying Mobile Objects in Spatio-Temporal Databases Kriengkrai Porkaew 1 Iosif Lazaridis 2 Sharad Mehrotra 2 1 King Monkut’s University of Technology at Thonburi, Thailand 2 University of California, Irvine SSTD 2001, Redondo Beach, CA

2. Talk Outline zRelated Work zQuery Types over Mobile Objects zIndexing & Query Evaluation Strategies yNative Space Indexing (NSI) yParametric Space Indexing (PSI) zExperiments zConclusions

3. Motivation - VGIS zVGIS ya 3D terrain visualization system zData yterrain, weather data, static & dynamic 3D objects zFunctionality yspatio-temporal queries over mobile objects

4. Update Model zLinear Motion with constant velocity zUpdate consists of zNext update arrives at time of previous update’s expiration t e. zBoth historical and future queries are supported time location

5. Related Work Spatio-Temporal Index Structures zTheodoridis et. al. SSDBM 1998 “Specifications for Efficient Indexing in Spatio-Temporal Databases” Indexing Mobile Objects zTayeb et. al. Computer Journal 41(3) “A quadtree based dynamic attribute indexing method” zKollios et. al. PODS 1999 “On Indexing Mobile Objects” zSaltenis et. al. SIGMOD 2000 “Indexing the Positions of Continuously Moving Objects” General zWolfson et. al. SSDBM 1998 “Moving Objects Databases: Issues and Solutions” Focus of Current Techniques: zFuture Spatio-Temporal Range Queries

6. Query Types Spatial/Temporal Range Which objects were in spatial range [Q.x L,Q.x iL ] during time interval [Q.t L,Q.t L ]? time location Q.t L Q.t H Q.x L Q.x H

7. Query Types Temporal kNN k top objects closest temporally to query time Q.t that lie in spatial range [Q.x L, Q.x H ], ordered by time time location Q.t 1 2 3 Q.x L Q.x H

8. Query Types Spatial kNN time location Q.t L 1 3 Q.t H 4 Q.x 2 k top objects closest spatial to query location Q.x during time interval [Q.t L, Q.t H ], ordered by proximity

9. Indexing Approaches Native Space Indexing (NSI) zrepresents objects with bounding boxes in native space (time/location) ybounding box: yL =R.t L,R.x 1L,…,R.x nL ; H=R.t H,R.x 1H,…,R.x nH L s e H X Time Object’s trajectory Y zTo eliminate false admission: yline-segment: ys=O.t s,O.x 1s,…,O.x ns ; e=O.t e,O.x 1e,…,O.x ne

10. zRange Query Q zFor a Bounding Box R: yif overlaps (Q, R), i.e., Q overlaps with R along the temporal and all spatial dimensions  explore node zFor a line segment L: yif L does not overlap with Q in time  ignore yelse … Native Space Indexing Range Query

11. Native Space Indexing Range Query – Line Segment time Q.x iH TiTi time O.T Q.T L i.T=time interval that the line of the object cuts the upper/lower boundary of the query along dimension i L i.T Q.x iL location T i =Q.T  O.T  L i.T T =  i T i — If T is empty, ignore — Else retrieve

12. k Nearest Neighbor Algorithm A B ABAB Priority Queue A CDECDE C D E BCDEBCDE B fghfgh f g h fCDEghfCDEgh f answer

13. Native Space Indexing Temporal kNN  Temporal kNN query:  retrieve objects in with minimum t=|Q.t-O.t|  explore nodes in ascending order of t using a priority queue zBounding Box testing yfor each i, if [R.x iL, R.x iH ] not overlap [Q.x iL, Q.x iH ]  ignore yelse, compute t and insert in the priority queue

14. Native Space Indexing Temporal kNN – Line Segment time location O.T L i.T TiTi Q.t T i = O.T  L i.T T ov =  i T i

15.  Spatial kNN query:  retrieve the k nearest objects to Q.x i during the time interval [ Q.t L, Q.t H ] yexplore node in ascending order of d = distance from Q.x i zBounding Box testing  if [ R.t L, R.t H ] not overlap [ Q.t L, Q.t H ]  ignore R yelse, compute d = mindist (P, Q) = [  I d i 2 ] 1/2 Native Space Indexing Spatial kNN xixi Q.x i d i =R.x L -Q.x H d i = Q.x L -R.x H d i =0 time Q Q Q Bounding Box Line Segment

16. Indexing Approaches Parametric Space Indexing (PSI) zrepresent objects with their motion parameters ê time ê starting location O.x i ê velocity O.v i zLocation Function O.x i (t)=O.x i +O.v i (t - O.t s ) where t s  t  t e zBounding box R= Velocity (v) Time (t) Location (x) Object’s motion Spatio-temporal Query (projected on a bounding box) zHistorical Queries feasible since past segments are kept in index zMaximum locality since t s the time reference of the most recent update is used

17. zBounding Box testing yif [Q.t L,Q.t H ] not overlap [R.t L,R.t H ]  ignore R; yelse compute time interval t ov,i that R overlaps Q in the native space along dimension i: T ov,i =T i  Q.T  R.T yif T ov,I is not empty on all dimensions, then explore R, else ignore it time v iH location TiTi Parametric Space Indexing Range Query Q.T v iL R.T R T ov,i

18. zBounding Box testing ycompute time interval T ov,i that R overlaps Q in the native space along dimension i T ov,i = T i  R.T T ov =  i T i v iH v iL time Bounding Box R t priority Parametric Space Indexing Temporal kNN Q.t TiTi R.T location T ov,i

19. yFirst, compute the temporal overlap: K.T= Q.T  R.T yThen, compute S i the extent of R in dimension i within the time range K.T yCompute s priority by taking the mindist of the query point Q.x i and the range S i and summing up over all dimensions Parametric Space Indexing Spatial kNN v iH time xixi Bounding Box R Query SiSi didi Q.x i v iL R.T Q.T K.T S priority = [  i d i 2 ] 1/2

20. Experiments zData y5,000 mobile objects moving in a 100x100 grid yObjects send ~1 update/time unit ySimulations with 1, 2, 4 velocity units were run yDuration of simulation 100 time units (~500,000 line segments in index) zQueries yRanges of sizes 0.25 to 10 along each spatial dim. yAverage results over 1,000-query loads

21. Range Queries I/O Cost

22. Range Queries CPU Cost

23. Range Queries Varying Object Speed

24. Temporal kNN I/O Cost

25. Spatial kNN I/O Cost

26. Interpretation Parametric Space Indexing + compact representation + no false alarms - need transformation - not so good locality - specific to the type of motion used Native Space Indexing + good locality + general for all kinds of motions: linear, circular, constant speed, constant acceleration + easy to deal with - highly overlapped boxes

27. Conclusions zClassification of selection queries over mobile objects with range or nearest neighbor predicate on space/time zQuery processing techniques using two indexing approaches: Native– and Parametric-Space Indexing zNative Space Indexing outperforms Parametric Space Indexing besides being conceptually simpler