STAR-Tree Spatio-Temporal Self Adjusting R-Tree

1. STAR-TreeSpatio-Temporal Self Adjusting R-Tree John Tran Duke University Department of Computer Science Adviser: Pankaj K. Agarwal

2. Problem • Large Moving Data Sets • Many static data structures exist, but not many account for motion, which is realistic

3. Examples of Use • Geographic Information Systems • Air-Traffic Control • Protein Interactions • Traffic Patterns

4. Defining the data • Can represent data as points in Rd • For our problem: • Set of data points in R2: S = {p1, p2, …, pn} • Can parameterize points to pi = (xi(t), yi(t)) • Piecewise differentiable velocities • Bounding boxes can be represented by 2 points

5. Queries • Query 1 – Report all points of S that lie inside rectangle R at time t

6. Queries • Query 2 – Report all points of S that lie inside rectangle R at any time between t1 and t2

7. Queries • Query 3 – Report the nearest neighbor of point  in S

8. R-Tree • Bounding Box Hierarchy • All Children nodes are bound by parents bounding box • Points are stored in leaf nodes

9. STAR-Tree • Same concept as R-Tree • Incorporate movement into tree structure

10. Conflicts • As bounding boxes change, overlap occurs • Need to adjust for these overlap conflicts

11. QT Implementation

12. OpenGL Implementation

13. Road Simplification • Road data from US Bureau of Census (TIGER) • Paths are determined using Dijkstra’s Shortest Path Algorithm • Shapes of these paths are typically simple but include many vertices • Simplify path using Douglas-Peucker heuristic (5 vertices max)

14. Road Simplification • Simplify road network • TIGER data is not perfect • Polygonal chain with vertex lists • Sometimes does not match roads that should be matched

15. Analysis of RDU Roads Vertices with n streets n streets

16. Analysis of RDU Roads Streets with n vertices n vertices

17. Road Simplification

18. Protein Shape Matching

19. Problem • Match two proteins based on similarity or dissimilarity using intramolecular distance comparison

20. Data • Start from PDB files • Parse to get vertex list

21. Calculating Distance Matrix • Given a vertex list

22. Calculating Distance Matrix • Given a vertex list

23. Defining cost -GCTGATACTAGCT | |||| ||||| GGGTGAT-GTAGCT • Let g(k) = +(k-1) •  is the cost of starting a new indel gap •  is the cost of continuing a gap

24. Cost Function • E(i,j) = min{D(i,j-1) + , E(i,j-1) + } • F(i,j) = min{D(i-1,j) + , F(i-1,j) + } • D(i,j) = min{D(i-1,j-1) + (i,j), E(i,j), F(i,j)} • Where (i,j) = normalized sum of difference distance between Ai and all the matched vertices and Bj to the corresponding matched vertices

25. Comparing identical Proteins

26. Test Cases