1 / 31

Topological Reasoning between Complex Regions in Databases with Frequent Updates

Topological Reasoning between Complex Regions in Databases with Frequent Updates. Arif Khan & Markus Schneider Department of Computer and Information Science and Engineering University of Florida Presented by: Hechen Liu. Motivation.

osmond
Télécharger la présentation

Topological Reasoning between Complex Regions in Databases with Frequent Updates

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Topological Reasoning between Complex Regions in Databases with Frequent Updates Arif Khan & Markus Schneider Department of Computer and Information Science and Engineering University of Florida Presented by: Hechen Liu

  2. Motivation • Topological relationships are important in many applications, e.g., AI, cognitive science, and spatial databases • It is impossible to find all topological facts • It is impractical to keep all topological facts • Simple regions are not enough to represent real life scenarios

  3. Complex Objects • Complex regions: • Multiple Components: faces • Each face may have single or multiple holes Interior: A◦ Exterior: A- Boundary: ∂A

  4. 9-Intersection Model

  5. 33 Relationships of Complex Regions [1] M. Schneider and T. Behr. Topological Relationships between Complex Spatial Objects. ACM Transactions on Database Systems, 31(1):39-81, 2006.

  6. Inference • Composition • Rx(A,B) , Ry(B,C)  Rz(A , C) • Rx o Ry  Rz • inside(A, B) o inside(B, C)  inside(A,C) • Determined by the inference rules

  7. Overview of the Reasoning Process • Local Inference • Apply inference rules • Interpret reasoning result and identify relationship(s) • Global Inference • Extend the inference to N complex regions • Binary Spatial Constraint Network (BSCN)

  8. Local Inference • Interior can characterize a complex region • 8 possible interior-interior set relations exist between two complex regions. A◊B: A∩ B≠  ∧ A- B≠  B- A≠  • 8*8=64 combinations possible between A and C.

  9. Inference Rules • Consider, • (A ⊂ B∧ ¬∂A∂B) ∧ (B⊂ C∧ ¬∂B∂C) • A ⊂ B ∧ B ⊂ C • A ⊂ C • A ∩ C ≠ ∅ • A ∩ C = 1 (interior-interior intersection) with the same input, • A ∩ C−= 0 (interior-exterior intersection) A B C C

  10. Inference Rules • Consider, A ◊Band B◊C • Ao ∩ Co= unknown (interior-interior intersection)

  11. Inference Rules

  12. Relationship Identifying Process • If all 9 predicates are deterministic, then inferred relationship is a single relationship. • If there is any unknown value, then the inferred relationship is a disjunction. For example:  

  13. Decision Tree of the Relation Space • Brute force method: 33*8=264 comparisons • Recursively divide the relationship space based on a predicate value at each level, until we reach a single relationship • e.g.,18 relationships have false in the interior-boundary (P2) value. • 33 relationships form a tree of height 6 • Deterministic values have 6 comparisons instead of 264: 97% improvement • Indeterminate values have at most 32 comparisons: 88% improvement

  14. Global Inference • Extend the reasoning process to N objects. • Binary Spatial Constraint Network (BSCN)

  15. Reasoning in Dynamic Databases • Find BSCN paths • Each time a change occurs in the database, the algorithm should run • Intermediate objects are thrown out when the query is committed

  16. Most Specific Relationship • The relationship which has the least number of disjunctions • Shortest path does not guarantee most specific relationship A E D C A B D B E C

  17. Most Specific Relationship • The relationship which has the least number of disjunctions. • Shortest path does not guarantee most specific relationship. overlap o overlap  unknown A C A B D B E C

  18. Most Specific Relationship • The relationship which has the least number of disjunctions • Shortest path does not guarantee most specific relationship inside o inside  inside A E D C A D B E C

  19. Most Specific Relationship • The relationship which has the least number of disjunctions • Shortest path does not guarantee most specific relationship • inside o disjoint  disjoint A E C A D B E C

  20. Most Specific Relationship • The relationship which has the least number of disjunctions • Shortest path does not guarantee most specific relationship • In fact, there is no relation between the length of the path and the most specific relationship

  21. Most Specific Relationship • Solution: consider all paths and take the intersection • Problem: number of paths is O(n!) • Interesting Facts: • Worst case scenario when the graph is complete (then, we even do not need reasoning) • Consider sparse graphs

  22. K-Shortest Paths • Let us not consider all the paths. Instead, we consider k-paths • K-shortest path algorithm: O(m+nlogn+k) [2] • Reasoning between complex regions: • Total complexity: O(n2log n) [2] D. Eppstein. Finding the k shortest paths. SIAM Journal on Computing, 28(2):652–673, 1999.

  23. Simulation and Result • Random graph • Edges are Power Law distributed • All edges have unit weight • Number of paths considered: k = cn

  24. Simulation and Results

  25. Conclusions and Future Work • Derived a complete set of inference rules • Proposed BSCN and a dynamic reasoning approach • Will introduce more robust heuristics • Weighted BSCN. • Will extend to other data types • line-line • line-region

  26. Questions and Comments? Please contact Mr. Arif Khan: ahkhan@cise.ufl.edu

  27. Thank you!

More Related