1. Spatio-temporal Pattern Queries M. Hadjieleftheriou G. Kollios P. Bakalov V. J. Tsotras

2. 2 Motivation The need to locate spatio-temporal objects that follow specific patterns. Examples:  Identify vehicles that were close to the three recent sniper incidents  Identify clients with specific credit card usage patterns  Analyze connectivity/mobility patterns in mobile ad-hoc networks (e.g., verify that a given pattern is prevalent)

3. 3 Example X Y T Q 2, t 2 Q 3, t 3 Q 1, t 1

4. 4 Formulation Syntax:  S can be any spatial predicate, T can be any temporal constraint or empty Score object trajectories according to how well they satisfy the query pattern Problem: Given a query pattern use an index to score trajectories incrementally Ideally: Access only parts of trajectories necessary to guarantee correct answers. Prune trajectories fast!

5. 5 Two Separate Problems STP Queries With Time  Every query predicate is associated with an absolute temporal constraint STP Queries With Order  Query predicates are associated with relative temporal constraint

6. 6 Types of STP Queries Range predicates: Crosses, Leaves, Meets, …  Use Boolean score functions (crosses or not) Distance based predicates: Nearest neighbor, Group nearest neighbor, all other neighbors, …  Use aggregate score functions (min, max, average, sum, …), as long as they are monotonic Combinations of the above  Use combined scoring functions and answer each group of queries individually

7. 7 STP Queries With Time We use existing spatio-temporal index structures to answer all predicates We employ concepts from T.A. (Fagin et al.) to answer predicates incrementally We prune trajectories according to upper and lower bounds We access the actual trajectories only when good candidates have been found

8. 8 A Simple Example P1P1 P2P2 Q P3P3 T X 0 2 -2 2 1 2 1 51 0

9. 9 A Simple Example P1P1 P2P2 Q P3P3 T X 0 2 -2 2 3 2 1 3

10. 10 STP Queries With Order X Y T Q2Q2 Q 3, t 3 Q 1, t 1 Q3Q3

11. 11 The Exact Distance is Expensive Cost increases exponentially as the number of predicates increases Can be computed more efficiently by using the T.A. algorithm Can we take predicate ordering into account and speed up T.A. as well?

12. 12 Previous Approaches Cannot Help Spatio-temporal indices cannot be used!  Full scan of temporal dimension of the index Projecting out the temporal dimension does not help! Ideally, we need to find a method that will retrieve only the trajectories that satisfy the predicates in the specified order

13. 13 Solution Decompose the space into a grid Keep a list of trajectory ids that intersect each grid cell, along with the respective time-periods Given the query predicates compose respective lists of trajectory ids/time- instants, from the constituent cells Use a merge-join algorithm to prune trajectories that do not satisfy the order of the query

14. 14 P1P1 P3P3 P2P2 The Index Structure A = { (P 1, 1) } A B... B = { (P 2, [2, 3]) } F = { (P 1, [3,4]), (P 2, 18) } … … This is the index that we will store

15. 15 Example P1P1 P3P3 P2P2 A B... Q1Q1 Q2Q2 1 3 5 (P 2, 2) (P 2, 7) Q1Q1 Q2Q2 (P 2, {2,3,15,16}), (P 1, {4,5}), (P 3, 5) U = {P 2 } 1 9 (P 2, {7,8,9,17,18}), (P 3, {3,4}) P

16. 16 Idea! Run T.A. using only the candidate trajectory data loaded so far to compute the exact distance Prove that the answer will be correct even if we don’t see the rest of the trajectory We speed up the computation cost associated with the queries as well!

17. 17 Experimental Evaluation Synthetic datasets on the freeways of Illinois Up to 500K objects and 6,000,000 MBRs Measure the average number of disk accesses for the index and the total number of candidate trajectories that need to be retrieved Compared linear scan, R-tree, MVR-tree

18. 18 STP Queries with Order Range Predicates

19. 19 STP Queries with Order Distance Based Predicates

20. 20 Conclusions Introduced a novel type of query Proposed a simple yet efficient expression mechanism Designed an efficient algorithm for STP Queries with Time Designed an efficient index structure and algorithms for STP Queries with Order Conducted extensive experiments

21. Thank you!