1. Data Management+ Laboratory V*-kNN: an Efficient Algorithm for Moving k Nearest Neighbor Queries Speaker: Adam Adviser: Yuling Hsueh 2009 IEEE International Conference on Data Engineering Sarana Nutanong, Rui Zhang, Egemen Tanin, Lars Kulik

2. INTRODUCTION  What is “Moving k Nearest Neighbor Queries(MkNN)” ? -K Nearest Neighbor Query(kNN) -Example of MkNN: Ambulance  Purpose: reduce the computation costs DM+  Page 2

3. INTRODUCTION  To avoid unnecessary data access(computation): Safe region  Safe region: a region in which the query point can move without changing the result  This V*-kNN is based on two types of safe regions, the fixed- rank region (FRR) and the safe region with regard to a data point DM+  Page 3

4. INTRODUCTION  Using a safe region-based method, an MkNN query can be processed :  (i) finding the current k NNs  (ii) calculating a region that the current k NNs are valid, i.e., a safe-region of the kNN;  (iii) repeating the first two steps when the query point moves out of the safe region. DM+  Page 4

5. Fixed-Rank Region  Compute regions (F(p1,p2,…,pn) or F(L)) where the ranking of all the objects (based on their distances) is the same  Need: list of points and corresponding list of bisectors  List of points: sorted in ascending order by their distances to the query point  Corresponding list of bisectors: for n points, it requires at most (n-1) bisectors of the (n-1) pairs of rank-adjacent points DM+  Page 5

6. Fixed-Rank Region DM+  Page 6  Each time the query point crosses a bisector, the ranks of the two corresponding points are swapped and the list of rank- adjacent bisectors are updated.  Only rank-adjacent points can swap their ranks

7. Fixed-Rank Region DM+  Page 7  (a, c, b, f, e, d), ( Bac, Bbc, Bbf, Bef, Bde )  (a, c, b, e, f, d), ( Bac, Bbc, Bbe, Bef, Bfd )

8. Safe Region With Regard To A Data Point  kNN  (k+x)NN, where x is the number of auxiliary points  assume that z is the farthest known point to qb, i.e., the (k + x)th NN of qb  Known region  Reliable  Reliable region : dist(q′, p) ≤ dist(qb, z) − dist(qb, q′).  Safe region with regard to the data point DM+  Page 8

9. Safe Region With Regard To A Data Point DM+  Page 9

10. V*-kNN  Combine Fixed-Rank Region with Safe Region With Regard To A Data Point  integrated safe region (ISR) DM+  Page 10

11. ALGORITHM DM+  Page 11

12. EXAMPLE DM+  Page 12

13. ADVANTAGES  The V*-kNN has the following key advantages:  (i) It requires no precomputation  (ii) It incrementally computes answers and therefore efficiently adapts to changes – such as insertions and deletions of objects, as well as, dynamically changing values of k DM+  Page 13

14. EXPERIMENT DM+  Page 14

15. THE END Thank you for listening! DM+  Page 15

16. THE END Q & A DM+  Page 16