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
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.scorek Λ vsf(onew)≤q.scorek)
Arrange the order of top-k list
Incoming update (vsf(oold)>q.scorek Λ vsf(onew)<q.scorek)
Insert the object into top-k list
Outgoing update (vsf(oold)≤q.scorek Λ 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??