indexing of network constrained moving objects
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DESCRIPTIONIndexing 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). - PowerPoint PPT Presentation
Indexing of Network Constrained Moving ObjectsDieter Pfoser Christian S. JensenChia-Yu Chang
Outline Introduction The Trajectory Case Reducing Dimensionality Performance Studies Conclusions
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.
Introduction (2/2)Three movement scenarios:1. Unconstrained movement (vessels at sea)2. Constrained movement (pedestrians)3. Movement in transportation networks (trains, cars)
The Trajectory CaseFirst approach: simply store the position.we couldnt answer queries about the objects movements at time s in-between those of the sampled positions.use linear interpolation
Indexing TrajectoryTrajectory 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.
Reducing DimensionalityTranslate 2D (network) into one Dimension.Translate 3D into two Dimensions.e.g., cars move on roads.Overall, we have to devise mappings for1. the Network2. the Trajectories3. the Queries
Network Mapping (1/2)Algorithm NetworkMapping (network)LOCALSrange //highest coordinatelow //lower coordinate of edge in 1D spaceup //upper coordinate of edge in 1D spaceNM1 sort edges by their FOR ALL edgesNM2 compute length of edgeNM3 low = range+ 1NM4 up = range+ 1+ lengthNM5 write edge(low, up)NM6 range = upEND FOR
Network Mapping (2/2)Algorithm NetworkMapping (network)FOR ALL edgesNM2 compute length of edgeNM3 low = range+ 1NM4 up = range+ 1+ lengthNM5 write edge (low, up)NM6 range = upEND FOR
Trajectory Mapping (1/2)Algorithm TrajectoryMapping (trajectory, 2Dnetwork, 1Dnetwork)FOR ALL segments of the trajectoryTM1 find traversed network edge in 2DnetworkTM2 det. traversed portion of edge in 2DnetworkTM3 x0, x1 = respective 1Dnetwork coordinatesTM4 write segment(x0, t0, x1, t1)END FOR
Trajectory Mapping (2/2)Algorithm TrajectoryMapping (trajectory, 2Dnetwork, 1Dnetwork)FOR ALL segments of the trajectoryTM1 find traversed network edge in 2DnetworkTM2 det. traversed portion of edge in 2DnetworkTM3 x0, x1 = respective 1Dnetwork coordinatesTM4 write segment(x0, t0, x1, t1)END FOR
Query MappingAlgorithm QueryMapping(query, 2Dnetwork)//2Dnetwork access using an R-tree structureQM1 given a query window, take the spatial extent and retrieve theportion contained in itQM2 lift the retrieved edges by the temporal extent of the query window
Performance Studies (1/9)Three synthetic networks:1. Hilbert network, h , 10232. Raster network, r2 , 5443. Parallel network, p , 33
Performance Studies (2/9)Two real networks:1. San Jose, CA , 241232. Oldenburg, Germany, 7035
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 36 for 3D and 51 for 2D indexes.Different types of networks.The impact of varying number of edges. r1 (144), r2 (544), r2 (2112), r4 (8320)
Performance Studies (4/9)500 moving objects which positions are sampled 250 times each. 125k trajectory segments 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%.
Performance Studies (5/9)Different types of synthetic networks:
Performance Studies (6/9)Networks of the same type but varying lengths and numbers of edges:
Performance Studies (7/9)Varying temporal extent for the Raster network:
Performance Studies (8/9)Different types of real networks:
Performance Studies (9/9)Different types of real networks:
ConclusionThe 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.