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Spatial and Spatio-temporal Networks Reem Ali, Amr Magdy

Spatial and Spatio-temporal Networks Reem Ali, Amr Magdy. Spatial Networks. Examples: Road, Train and River networks. Data Models. Conceptual Data Model Graphs Logical Data Model Data types: Graph, Vertex, Edge, Path, … Operations: addEdge (), getSuccessors (), ... Physical Data Model

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Spatial and Spatio-temporal Networks Reem Ali, Amr Magdy

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  1. Spatial and Spatio-temporal Networks Reem Ali, Amr Magdy

  2. Spatial Networks • Examples: Road, Train and River networks

  3. Data Models • Conceptual Data Model • Graphs • Logical Data Model • Data types: Graph, Vertex, Edge, Path, … • Operations: addEdge(), getSuccessors(), ... • Physical Data Model • Memory based: Adjacency list, Adjacency Matrix • Disk based: normalized and denormalized

  4. Data Models (cont’d) • Normalized Representation • Denormalized Representation

  5. Query Languages for Graphs • Relational Algebra-based languages cannot compute “Transitive Closure” • Support for Graph Queries: • CONNECT (SQL92 for DAG) • RECURSIVE (SQL3) Transitive Closure

  6. Graph Algorithms • Traversal: Breadth First Search, Depth First Search • Shortest Path: Dijkstra’s and Best First • Large graphs cannot fit in main memory => Hierarchical Strategies • Boundary Graph • Fragment Graphs

  7. Access Methods • We need to minimize I/O cost for graph algorithms. • e.g. getSuccessors() is a dominant I/O cost for many queries • Connectivity Residue Ratio (CRR)= total no. of unsplit edges/total no. of edges • Graph Partitioning: to maximize CRR. • e.g. CCAM

  8. Spatio-temporal Networks • Definition: a network whose status changes with time • e.g., road networks status changes from time to another due to traffic changes • e.g., air travel paths changes due to weather conditions

  9. Applications • Road Networks • e.g., Emergency traffic planning, route finding services, Minimizing travel times, Freight Delivery Services, etc. • Air travel networks • e.g., flight route planning

  10. Representations • Snapshot-based Graph Collection • Time-expanded Graph A A 2 A 1 C C C 3 1 2 3 B 1 B B at t=0 at t=1 at t=2 t=0 t=2 t=1 t=3 t=4 t=5 A0 A2 A1 A3 A4 A5 B0 B2 B1 B3 B4 B5 C0 C2 C1 C3 C4 C5

  11. Representations • Time-aggregated Graph A [1,2,-] C [2,3,1] [1,-,3] B

  12. Important Problems • Fixed start-time shortest path • All start-times shortest path • Recommending best travel start-time

  13. All Start Times Shortest Paths • Shortest path does not change every time instant • Instead, each interval of time hasshortest path e.g., rush vs. non-rush hour • One path calculation is required per interval(big computation saving) • Start time instants when the shortest path between a source and destination may change are called critical time points

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