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Handling Spatial Data In P2P Systems

Handling Spatial Data In P2P Systems. Verena Kantere, Timos Sellis, Yannis Kouvaras. Problem Definition. Assumptions: Structure P2P Overlays Spatial Data in Peers Problem: Necessity for indexing and routing techniques for such an environment. Technique Requirements.

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Handling Spatial Data In P2P Systems

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  1. Handling Spatial Data In P2P Systems Verena Kantere, Timos Sellis, Yannis Kouvaras

  2. Problem Definition Assumptions: • Structure P2P Overlays • Spatial Data in Peers • Problem: • Necessity for indexing and routing techniques for such an environment

  3. Technique Requirements We need a technique that: • Guarantees the retrieval of any existing spatial information in the system • Achieves satisfying index size for any node • Achieves a satisfying length for any search path • Provides easier access to popular information • Preserves proximity of areas

  4. Related Work • P2PR-tree (Workshop of EDBT ‘04) • Quad-tree approach (Poster in ICDE’05) • kd-tree approach (WebDB’04)

  5. Partitioning Space Spatial Coding

  6. Partitioning Space cont’d The code of an area A is: • A  azaxay • az: is the granularity level, i.e. the size in terms of cells. • ax: is the average of the digit d1 of all the area cells. • ay: is the average of the digit d2 of all the area cells. Distance Metrics: d1(A1, A2) = |a1x-a2x|+|a1y-a2y| d2(A1, A2) = ||a1x-a2x|-|a1y-a2y|| D(A1, A2)  d1d2 Dzoom(A1, A2)  D(A1, A2)/(0.5*|A1.az+A2.az|)

  7. Distributed Indexing for Spatial Areas Distributed Indexing Algorithm • Step 1: Indexing the grids of each level • Phase A: Indexing areas of the same grid • Phase B: Indexing areas of other grids of the same level • Step 2: Indexing the grids of other levels

  8. Grid Example

  9. Direct Neighbors &Data Hashing Peers have 2 neighbors on each dimension: • Horizontal • Vertical • Perpendicular Neighbors are the closest peers on each direction. Areas are stored to the closest neighbor following a priorities of dimensions

  10. Direct Neighbors: Examples

  11. Routing of Spatial Queries Basic Routing Algorithm Step 1: Find a peer corresponding to the same size as the sought area. Step 2: Find a peer hosting the sought area or an overlapping area of the latter Step 3: Find the peer hosting the sought area

  12. Routing Example

  13. Details…

  14. Complexity Characteristics Complexity for both pure Chord and our method is O(3log2n). But with our method: • Peers with big areas are favored with small indexes • Shorter search paths for bigger areas • The search path grows with the relative distance

  15. Assignment of Peer IDs The peer ID plays a significant role in our approach joining peers can ask for specific ids: • it is adequate to assign an id that belongs to the same or similar level as the requested id • The above constraint loosens with the size of the area (higher levels are more connected)

  16. Preliminary Experiments

  17. Preliminary Experiments (2)

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