A Unified Algorithm for Continuous Monitoring of Spatial Queries

1. A Unified Algorithm for Continuous Monitoring of Spatial Queries Presented by: Muhammad Aamir Cheema Joint work with Mahady Hasan, Xuemin Lin, Wenjie Zhang University of New South Wales, Australia

2. Introduction • No existing unified algorithm • Our unified algorithm • answers a broad class of spatial queries • for each query, we only need to change the scoring function Presented by: Muhammad Aamir Cheema

3. Problem definition Versatile scoring function • Let f(p) be a function that returns the score of a point p • Upper bound score of a rectangle R is • Lower bound score is • The function f( ) is called versatile iff SU(R) ≥ SU (Rc) and SL(R) ≤ SL (Rc) for every R and its child rectangle Rc R p Rc q f(p) = dist(p,q) f(p) = - dist(p,q) Presented by: Muhammad Aamir Cheema

4. Problem definition Versatile top-k query • Return k objects with smallest scores Continuous versatile top-k query • Continuously report top-k objects as the dataset changes R p Rc q f(p) = dist(p,q) Presented by: Muhammad Aamir Cheema

5. Related Work k Nearest Neighbors query Return k objects closest to the query point • SEA-CNN [ICDE05] • YPK [ICDE05] • CPM [SIGMOD05] • CircularTrip [DASFAA 07] • iSEE [SSDBM 07] Presented by: Muhammad Aamir Cheema

6. Related Work k Furthest Neighbors query Return k objects furthest from the query point • [JCSS89] • [PR98] • [WALCOM09] Presented by: Muhammad Aamir Cheema

7. Related Work Constrained k Nearest Neighbors query Return k objects closest to the query point among the objects that lie in a constrained region • [SSTD01] • [DASFAA10] Presented by: Muhammad Aamir Cheema

8. Related Work Aggregate k Nearest Neighbors query Given a set of query points, return k objects that have smallest aggregated distance. • [TKDE05] • [SIGMOD05] • [ICCSA07] Presented by: Muhammad Aamir Cheema

9. Modeling spatial queries to versatile top-k queries k nearest neighbors query • f(p) = dist(p,q) k furhtest neighbors query • f(p) = - dist(p,q) Constrained k nearest neighbors query • If p is inside the constrained region • f(p) = dist(p,q) • Else • f(p) = ∞ Presented by: Muhammad Aamir Cheema

10. Modeling spatial queries to versatile top-k queries Aggregate k nearest neighbors query • Sum • Max • Min Presented by: Muhammad Aamir Cheema

11. Conceptual Grid-Tree root Intermediate Entries Grid Cells Presented by: Muhammad Aamir Cheema

12. Initial Computation • Insert root of grid-tree in heap with key set to zero • While heap is not empty • de-heap a rectangle R • If SL(R) > q.scorek • Return top-k objects • If R is a cell of the grid • Retrieve the objects in R and update top-k list and q.scorek • Else • For each child Rc of R • If SL(Rc) ≤ q.scorek • insert Rc in heap with key SL(Rc) Presented by: Muhammad Aamir Cheema

13. Continuous monitoring • Phase 1: receive object and query updates. • Change in the queries based on the update below. • Internal update (vsf(oold)≤q.scorekΛ vsf(onew)≤q.scorek) • Arrange the order of top-k list Incoming update (vsf(oold)>q.scorekΛ vsf(onew)<q.scorek) • Insert the object into top-k list • Outgoing update (vsf(oold)≤q.scorekΛ vsf(onew)>q.scorek) • Remove the object from top-k list Presented by: Muhammad Aamir Cheema

14. Continuous monitoring … • Phase 2: Check the status of each query one by one • If query moved then • Execute the initial algorithm. • If top-k list contains at least k objects then • Keep top k objects and remove rest of the objects. • If top-k list contains less than k objects then • Expand the search area by visiting more cells Presented by: Muhammad Aamir Cheema

15. Experiments • We compare our algorithm with CPM [SIGMOD05] • Moving objects are generated using Brinkhoff generator [GeoInformatica02] Presented by: Muhammad Aamir Cheema

16. Effect of grid size Presented by: Muhammad Aamir Cheema

17. Effect of k Presented by: Muhammad Aamir Cheema

18. Effect of agility Presented by: Muhammad Aamir Cheema

19. Aggregate kNN queries Presented by: Muhammad Aamir Cheema

20. Thank you… Questions??