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Indexing of Network Constrained Moving Objects

Indexing of Network Constrained Moving Objects. Dieter Pfoser Christian S. Jensen. Chia-Yu Chang. Outline. Introduction The Trajectory Case Reducing Dimensionality Performance Studies Conclusions. time. y. x. Introduction (1/2).

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Indexing of Network Constrained Moving Objects

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  1. Indexing of Network Constrained Moving Objects Dieter Pfoser Christian S. Jensen Chia-Yu Chang

  2. Outline • Introduction • The Trajectory Case • Reducing Dimensionality • Performance Studies • Conclusions

  3. time y x Introduction (1/2) • Concern with the indexing of the movements of mobile objects for post-processing (e.g. data mining) purpose. • The movement of an object may be represented by a trajectory, or polyline, in the three dimensional (x, y, t) space.

  4. Introduction (2/2) • Three movement scenarios: 1. Unconstrained movement (vessels at sea) 2. Constrained movement (pedestrians) 3. Movement in transportation networks (trains, cars)

  5. The Trajectory Case • First approach: simply store the position. →we couldn’t answer queries about the object’s movements at time s in-between those of the sampled positions. →use linear interpolation

  6. Indexing Trajectory • Trajectory are 3D spatial entities, and they can be indexed using spatial methods. • The R-tree approximates the data objects by Minimum Bounding Boxes (MBBs). • Large amounts of “dead space”.

  7. Reducing Dimensionality • Translate 2D (network) into one Dimension. • Translate 3D into two Dimensions. e.g., cars move on roads. • Overall, we have to devise mappings for 1. the Network 2. the Trajectories 3. the Queries

  8. Network Mapping (1/2) • Algorithm NetworkMapping (network) LOCALS range //highest coordinate low //lower coordinate of edge in 1D space up //upper coordinate of edge in 1D space NM1 sort edges by their FOR ALLedges NM2 compute length of edge NM3 low = range+ 1 NM4 up = range+ 1+ length NM5 write edge(low, up) NM6 range = up END FOR Hilbert value

  9. Network Mapping (2/2) • Algorithm NetworkMapping (network) FOR ALLedges NM2 compute length of edge NM3 low = range+ 1 NM4 up = range+ 1+ length NM5 write edge (low, up) NM6 range = up END FOR

  10. Trajectory Mapping (1/2) • Algorithm TrajectoryMapping (trajectory, 2Dnetwork, 1Dnetwork) FOR ALLsegments of the trajectory TM1 find traversed network edge in 2Dnetwork TM2 det. traversed portion of edge in 2Dnetwork TM3 x0, x1 = respective 1Dnetwork coordinates TM4 write segment(x0, t0, x1, t1) END FOR

  11. Trajectory Mapping (2/2) • Algorithm TrajectoryMapping (trajectory, 2Dnetwork, 1Dnetwork) FOR ALLsegments of the trajectory TM1 find traversed network edge in 2Dnetwork TM2 det. traversed portion of edge in 2Dnetwork TM3 x0, x1 = respective 1Dnetwork coordinates TM4 write segment(x0, t0, x1, t1) END FOR

  12. Query Mapping • Algorithm QueryMapping(query, 2Dnetwork) //2Dnetwork access using an R-tree structure QM1 given a query window, take the spatial extent and retrieve the portion contained in it QM2 lift the retrieved edges by the temporal extent of the query window

  13. Performance Studies (1/9) • Three synthetic networks: 1. Hilbert network, “h” , 1023 2. Raster network, “r2” , 544 3. Parallel network, “p” , 33

  14. Performance Studies (2/9) • Two real networks: 1. San Jose, CA , 24123 2. Oldenburg, Germany, 7035

  15. Performance Studies (3/9) • Index structure for 3D and 2D Trajectory:R-Tree implementation in C. • Page size of each node is 1024 bytes which results in maximum fanouts of 36for 3D and 51for 2D indexes. • Different types of networks. • The impact of varying number of edges. → r1 (144), r2 (544), r2 (2112), r4 (8320)

  16. Performance Studies (4/9) • 500 moving objects which positions are sampled 250 times each. → 125k trajectorysegments each. • Sizes of 2D and 3D indexes are 2.5MB and 3.35MB. • 500 quadratic query windows, each with spatial extents of 0.25%, 0.5%, 1%, 2%, 4%, and 8% of the quadratic 2D space. • Temporal extent of the query was kept constant at 10%.

  17. Performance Studies (5/9) • Different types of synthetic networks:

  18. Performance Studies (6/9) • Networks of the same type but varying lengths and numbers of edges:

  19. Performance Studies (7/9) • Varying temporal extent for the Raster network:

  20. Performance Studies (8/9) • Different types of real networks:

  21. Performance Studies (9/9) • Different types of real networks:

  22. Conclusion • The dimensionality of trajectories can be reduced from three to two. • The number of 2D queries that result from the mapping of a 3D query is critical. The larger it is, the less likely it is that the mapping approach outperforms querying data in the original space. • The lower complexity of a network, the more likely the mapping approach proves to be beneficial over indexing the data in 3D space.

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