Efficient Spatial Sampling of Large Geographical Tables

90-minute presentation at the InfoCloud (cloud.kaust.edu.sa) group meeting, on "Efficient Spatial Sampling of Large Geographical Tables" by Anish Das Sarma et al., published in SIGMOD '12 and TODS '13.

Transcript

1. Efficient Spatial Sampling of Large Geographical Tables (SIGMOD ‘12 / TODS ‘13) Anish Das Sarma, Hongrae Lee, Hector Gonzalez, Jayant Madhavan, Alon Halevy Google Research Presented by Emaad Ahmed Manzoor March 10, 2014
2. Thinning
3. Constraints Objectives Challenges
6. Definitions
7. Definitions
8. Visibility Zoom Consistency Adjacency Constraints
10. The Thinning Problem
11. K = 1 M1 = { 4, 4, 4, 4, 4 } M2 = { 1, 3, 4, 4, 4 } M3 = { 2, 3, 4, 4, 4 }
12. Maximality Fairness Importance Objectives
13. K = 1 M1 = { 4, 4, 4, 4, 4 } M2 = { 1, 3, 4, 4, 4 } M3 = { 2, 3, 4, 4, 4 }
14. Problem Maximality Fairness Importance Visibility Zoom Consistency Adjacency Constraints Objectives
15. Problem Maximality Fairness Importance Visibility Zoom Consistency Adjacency Constraints Objectives Optimization
16. Integer Programming
17. Variables
19. Sampling Constraints
20. Zoom Consistency & Visibility Constraints
21. Thinning solution
23. Program Size
29. Critical nodes
31. Bounded Cover
32. Critical nodes
33. Program Size
34. Relaxing Integer Constraints
35. Objectives
36. Maximality
37. Strong Maximality There does not exist M’ such that:
38. K = 1 M1 = { 4, 4, 4, 4, 4 } M2 = { 1, 3, 4, 4, 4 } M3 = { 2, 3, 4, 4, 4 } M4 = { 1, 4, 4, 4, 3 }
39. Strong Maximality is NP-Hard
40. Weak Maximality There does not exist M’ such that: for some 1 <= i <= n
41. K = 1 M1 = { 4, 4, 4, 4, 4 } M2 = { 1, 3, 4, 4, 4 } M3 = { 2, 3, 4, 4, 4 } M4 = { 1, 4, 4, 4, 3 }
43. DFS
46. K = 1 M2 = { 1, 3, 4, 4, 4 }
47. Point-only Datasets
49. Experiments
50. 2.67GHz quad-core 12GB (starting at 1GB, or 4GB for the scalability tests) Java 1.6 Apache Simplex K=500 “Some plots were too big, so we threw them out.”
51. Program Size
53. Integer Relaxation
54. Scalability
56. Objectives
59. Takeaways
60. Use DFS if you care only about maximality Otherwise use the minimised LP The randomized points-only algorithm consumes constant memory and scales arbitrarily (not shown)
61. .