List of Figures

1. Google Maps (http://maps.google.com)
2. Difficulty in Finding the Spatial Proximity of Objects
3. Effect of Different Distance Definitions on Nearest Neighbors
4. An Example of a NN Query on R-tree Index
5. YPK-CNN
6. SEA-CNN
7. CPM
8. Example of Safe Regions
9. Threshold-Based Algorithm for Monitoring a 3-NN Query
10. The Objects $a$ and $e$ are the Reverse Nearest Neighbors of $q$
11. Illustration of SAA
12. Half-Plane Pruning
13. The Monitoring Region of a Continuous RNN Query
14. Illustration of $mindist(q,M,R)$ and $minmaxdist(q,M,R)$
15. Computation of a Constrained Nearest Neighbor Query
16. Node $N_1$ can be pruned
17. Different Pruning Metrics for All-NN Queries
18. Grid Index
19. Minimal Set of Cells
20. CircularTrip
21. Next Intersected Cell is Either $c_c$ or $c_N$
22. Minimum Angular Distance
23. ArcTrip
24. The Special Cell $c_{spe}$ is Always the Adjacent Cell of $c$ in $D_{opp}$
25. System Overview and Data Structure
26. A Nearest Neighbor Query
27. Handling Data Point Updates
28. Handling Query Updates
29. Handling Multiple Updates
30. Updating Influence Region
31. An Example of Updates Handling by CPM
32. An Example of Updates Handling by CircularTrip-based Algorithm
33. Effect of $\delta$
34. Effect of $k$
35. Effect of $N$ and $n$
36. Data Movement
37. Query Movement
38. Time Efficiency
39. Six Pie-Region Constrained NN Queries
40. A Continuous Pie-Region $1$ -CNN query
41. A Varying Pie-Region Continuous $1$ -CNN Query
42. A Donut-Region $k$ CNN Query
43. Computation of a Donut-Region $1$ -CNN Query
44. A Varying Donut-Region Continuous $1$ -CNN query
45. Donut-Pie $k$ CNN Query
46. Computation of a Donut-Pie $1$ -CNN Query
47. Computation of a Varying Donut-Pie Region $1$ -CNN Query
48. Continuous $k$ CNN Query Over Irregular Region $R$
49. Computation of a Farthest Nearest Neighbor Query
50. Update Handling of a Farthest Neighbor Query
51. A ($k+m$ )NNs Query ($k=3, m=2$ )