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Active Nearest N eighbor Queries for Moving Objects

Active Nearest N eighbor Queries for Moving Objects

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Active Nearest N eighbor Queries for Moving Objects

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  1. Active Nearest Neighbor Queriesfor Moving Objects Jan Kolar, Igor Timko The Fourth WIM Meeting

  2. Outline • Problem Statement • System Architecture • Data Model • Tracking Moving Objects • NNC Search & Active Result • Distance between Moving Points • Conclusions • Proposals for Bachelor Projects The Fourth WIM Meeting

  3. Problem Statement • Road Network Copenhagen • Moving Data Points Cars, pedestrians, cyclists, ... • Distance along the roads • Query Point A shop assistant • Active K-Nearest Neighbor Query Monitor 2 nearest shoppers that need a nice and cheap dress • Active Query Result T1 : <A, B> T2 : <B, C> The Fourth WIM Meeting

  4. Problem Statement • Road Network Copenhagen • Moving Data Points Cars, pedestrians, cyclists, ... • Distance along the roads • Query Point A shop assistant • Active K-Nearest Neighbor Query Monitor 2 nearest shoppers that need a nice and cheap dress • Active Query Result T1 : <A, B> T2 : <B, C> The Fourth WIM Meeting

  5. Problem Statement • Road Network Copenhagen • Moving Data Points Cars, pedestrians, cyclists, ... • Distance along the roads • Query Point A shop assistant • Active K-Nearest Neighbor Query Monitor 2 nearest shoppers that need a nice and cheap dress • Active Query Result T1 : <A, B> T2 : <B, C> The Fourth WIM Meeting

  6. Problem Statement • Road Network Copenhagen • Moving Data Points Cars, pedestrians, cyclists, ... • Distance along the roads • Query Point A shop assistant • Active K-Nearest Neighbor Query Monitor 2 nearest shoppers that need a nice and cheap dress • Active Query Result T1 : <A, B> T2 : <B, C> The Fourth WIM Meeting

  7. Problem Statement • Road Network Copenhagen • Moving Data Points Cars, pedestrians, cyclists, ... • Query Point A shop assistant • Active K-Nearest Neighbor Query Monitor 2 nearest shoppers that need a nice and cheap dress • Active Query Result T1 : <A, B> T2 : <B, C> • Distance along the roads The Fourth WIM Meeting

  8. Problem Statement • Road Network Copenhagen • Moving Data Points Cars, pedestrians, cyclists, ... • Distance along the roads • Query Point A shop assistant • Active K-Nearest Neighbor Query Monitor 2 nearest shoppers that need a nice and cheap dress • Active Query Result T1 : <A, B> T2 : <B, C> A ? B C The Fourth WIM Meeting

  9. Problem Statement • Road Network Copenhagen • Moving Data Points Cars, pedestrians, cyclists, ... • Distance along the roads • Query Point A shop assistant • Active K-Nearest Neighbor Query Monitor 2 nearest shoppers that need a nice and cheap dress • Active Query Result T1 : <A, B> T2 : <B, C> Time T1 A ? B C The Fourth WIM Meeting

  10. Problem Statement • Road Network Copenhagen • Moving Data Points Cars, pedestrians, cyclists, ... • Distance along the roads • Query Point A shop assistant • Active K-Nearest Neighbor Query Monitor 2 nearest shoppers that need a nice and cheap dress • Active Query Result T1 : <A, B> T2 : <B, C> Time T1 A ? B C The Fourth WIM Meeting

  11. Problem Statement • Road Network Copenhagen • Moving Data Points Cars, pedestrians, cyclists, ... • Distance along the roads • Query Point A shop assistant • Active K-Nearest Neighbor Query Monitor 2 nearest shoppers that need a nice and cheap dress • Active Query Result T1 : <A, B> T2 : <B, C> Time T1 A ? B C The Fourth WIM Meeting

  12. Problem Statement • Road Network Copenhagen • Moving Data Points Cars, pedestrians, cyclists, ... • Distance along the roads • Query Point A shop assistant • Active K-Nearest Neighbor Query Monitor 2 nearest shoppers that need a nice and cheap dress • Active Query Result T1 : <A, B> T2 : <B, C> Time T1 A ? B C The Fourth WIM Meeting

  13. Problem Statement • Road Network Copenhagen • Moving Data Points Cars, pedestrians, cyclists, ... • Distance along the roads • Query Point A shop assistant • Active K-Nearest Neighbor Query Monitor 2 nearest shoppers that need a nice and cheap dress • Active Query Result T1 : <A, B> T2 : <B, C> Time T2 A B ? C The Fourth WIM Meeting

  14. Problem Statement • Road Network Copenhagen • Moving Data Points Cars, pedestrians, cyclists, ... • Distance along the roads • Query Point A shop assistant • Active K-Nearest Neighbor Query Monitor 2 nearest shoppers that need a nice and cheap dress • Active Query Result T1 : <A, B> T2 : <B, C> Time T2 A B ? C The Fourth WIM Meeting

  15. Problem Statement • Road Network Copenhagen • Moving Data Points Cars, pedestrians, cyclists, ... • Distance along the roads • Query Point A shop assistant • Active K-Nearest Neighbor Query Monitor 2 nearest shoppers that need a nice and cheap dress • Active Query Result T1 : <A, B> T2 : <B, C> Time T2 A B ? C The Fourth WIM Meeting

  16. Problem Statement • Road Network Copenhagen • Moving Data Points Cars, pedestrians, cyclists, ... • Distance along the roads • Query Point A shop assistant • Active K-Nearest Neighbor Query Monitor 2 nearest shoppers that need a nice and cheap dress • Active Query Result T1 : <A, B> T2 : <B, C> Time T2 A B ? C The Fourth WIM Meeting

  17. System Architecture SERVER CLIENT NNC Request NNC Search Active Result User Query NNC Reply NNC Refresh Positioning Unit DB of Moving Points Position Update Client Position Road Network Road Network RN Update RN Input DB of Distances Visualization Result The Fourth WIM Meeting

  18. System Architecture SERVER CLIENT NNC Request NNC Search Active Result User Query NNC Reply NNC Refresh Positioning Unit DB of Moving Points Position Update Client Position Road Network Road Network RN Update RN Input DB of Distances Visualization Result The Fourth WIM Meeting

  19. System Architecture SERVER CLIENT NNC Request NNC Search Active Result User Query NNC Reply NNC Refresh Positioning Unit DB of Moving Points Position Update Client Position Road Network Road Network RN Update RN Input DB of Distances Visualization Result The Fourth WIM Meeting

  20. System Architecture SERVER CLIENT NNC Request NNC Search Active Result User Query NNC Reply NNC Refresh Positioning Unit DB of Moving Points Position Update Client Position Road Network Road Network RN Update RN Input DB of Distances Visualization Result The Fourth WIM Meeting

  21. Outline • Problem Statement • System Architecture • Data Model • Tracking Moving Objects • NNC Search & Active Result • Distance between Moving Points • Conclusions • Proposals for Bachelor Projects The Fourth WIM Meeting

  22. Data Model : Overview • Problem Data • Road Network (RN) • Data Points (DPs) • 2D Representation • Captures data in native form • Supports positioning and visualization • Source for graph representation • Graph Representation • Captures data in simpler and more ”compact” form • Supports algorithms for NN search The Fourth WIM Meeting

  23. Data Model : Overview • Problem Data • Road Network (RN) • Data Points (DPs) • 2D Representation • Captures data in native form • Supports positioning and visualization • Source for graph representation • Graph Representation • Captures data in simpler and more ”compact” form • Supports algorithms for NN search The Fourth WIM Meeting

  24. Data Model : Overview • Problem Data • Road Network (RN) • Data Points (DPs) • 2D Representation • Captures data in native form • Supports positioning and visualization • Source for graph representation • Graph Representation • Captures data in simpler and more ”compact” form • Supports algorithms for NN search The Fourth WIM Meeting

  25. Data Model : Overview • Problem Data • Road Network (RN) • Data Points (DPs) • 2D Representation • Captures data in native form • Supports positioning and visualization • Source for graph representation • Graph Representation • Captures data in simpler and more ”compact” form • Supports algorithms for NN search The Fourth WIM Meeting

  26. Data Model : Road Network • Real-World RN • Road segments • 2D RN • Lines approximate road segments • Lines start and end at vertices • Vertices have coordinates • Graph RN • Edges are obtained from paths • Edges start and end at nodes • Nodes have no coordinates Road Network 2D Graph The Fourth WIM Meeting

  27. Data Model : Road Network • Real-World RN • Road segments • 2D RN • Lines approximate road segments • Lines start and end at vertices • Vertices have coordinates • Graph RN • Edges are obtained from paths • Edges start and end at nodes • Nodes have no coordinates Road Network 2D Graph The Fourth WIM Meeting

  28. Data Model : Road Network • Real-World RN • Road segments • 2D RN • Lines approximate road segments • Lines start and end at vertices • Vertices have coordinates • Graph RN • Edges are obtained from paths • Edges start and end at nodes • Nodes have no coordinates Road Network 2D Graph The Fourth WIM Meeting

  29. Data Model : Road Network • Real-World RN • Road segments • 2D RN • Lines approximate road segments • Lines start and end at vertices • Vertices have coordinates • Graph RN • Edges are obtained from paths • Edges start and end at nodes • Nodes have no coordinates Road Network 2D Graph The Fourth WIM Meeting

  30. Data Model : RN Characteristics • Real-World RN • Road segments have length, maximum speed, and width • 2D RN • Lines approximate road segments • Lines have length and maximum speed • Lines have no width • Graph RN • Edges are obtained from paths • Edges have edge weight • Edge weight is minimal travel time along the edge – distance in graph • Edge weight is calculated by combining line length and maximum speed Road Network 2D Graph The Fourth WIM Meeting

  31. Data Model : RN Characteristics • Real-World RN • Road segments have length, maximum speed, and width • 2D RN • Lines approximate road segments • Lines have length and maximum speed • Lines have no width • Graph RN • Edges are obtained from paths • Edges have edge weight • Edge weight is minimal travel time along the edge – distance in graph • Edge weight is calculated by combining line length and maximum speed Road Network 2D Graph The Fourth WIM Meeting

  32. Data Model : RN Characteristics • Real-World RN • Road segments have length, maximum speed, and width • 2D RN • Lines approximate road segments • Lines have length and maximum speed • Lines have no width • Graph RN • Edges are obtained from paths • Edges have edge weight • Edge weight is minimal travel time along the edge – distance in graph • Edge weight is calculated by combining line length and maximum speed Road Network L=10 MS=2 L=12 MS=4 L=10 MS=5 2D Graph The Fourth WIM Meeting

  33. Data Model : RN Characteristics • Real-World RN • Road segments have length, maximum speed, and width • 2D RN • Lines approximate road segments • Lines have length and maximum speed • Lines have no width • Graph RN • Edges are obtained from paths • Edges have edge weight • Edge weight is minimal travel time along the edge – distance in graph • Edge weight is calculated by combining line length and maximum speed Road Network L=10 MS=2 L=12 MS=4 L=10 MS=5 2D W=2+3+5=10 Graph The Fourth WIM Meeting

  34. Data Model : Data Points • Real-World DPs • Movement of a DP is a continuous function of time • 2D Road DPs • A DP at a reference time is given by DP characteristics (DPC): • reference time • coordinate • speed Road Network 2D The Fourth WIM Meeting

  35. Data Model : Data Points • Real-World DPs • Movement of a DP is a continuous function of time • 2D Road DPs • A DP at a reference time is given by DP characteristics (DPC): • reference time • coordinate • speed C(12)=(33,60) Road Network 2D The Fourth WIM Meeting

  36. Data Model : Data Points • Real-World DPs • Movement of a DP is a continuous function of time • 2D Road DPs • A DP at a reference time is given by DP characteristics (DPC): • reference time • coordinate • speed C(12)=(33,60) Road Network T=11 C=(34,56) S=3 2D The Fourth WIM Meeting

  37. Data Model : Data Points • 2D Road DPs • A DP at the reference time is given by DP characteristics (DPC): • reference time • coordinate • speed • Graph DPs • Movement of a DP is a function of time (positioning function) • Positioning function is a combination of DPC: • reference time • edge • initial position • graph speed T=11 C=(34,56) S=3 2D T=11 E=3 IP=3 GS=3 Graph The Fourth WIM Meeting

  38. Data Model : Data Points • 2D Road DPs • A DP at the reference time is given by DP characteristics (DPC): • reference time • coordinate • speed • Graph DPs • Movement of a DP is a function of time (positioning function) • Positioning function is a combination of DPC: • reference time • edge • initial position • graph speed T=11 C=(34,56) S=3 2D P(12)=3+3 = 6 T=11 E=3 IP=3 GS=3 Graph The Fourth WIM Meeting

  39. Outline • Problem Statement • System Architecture • Data Model • Tracking Moving Objects • NNC Search & Active Result • Distance between Moving Points • Conclusions • Proposals for Bachelor Projects The Fourth WIM Meeting

  40. System Architecture SERVER CLIENT NNC Request NNC Search Active Result User Query NNC Reply NNC Refresh Positioning Unit DB of Moving Points Position Update Client Position Road Network Road Network RN Update RN Input DB of Distances Visualization Result The Fourth WIM Meeting

  41. Th Th Th Th Th Th Th Th Deviation Deviation Start End Node P(C) P(C) Node P(C)=P(S) P(C)=P(S) P(S) P(S) Tracking Moving Points • For a DP, its Client DPC are obtained from the Positioning Unit on the Client • For a DP, its Server DPC reside in the DB of Moving Points on the Server • Update Policy • Threshold is a maximum allowed deviation between the positions given by the Client DPC and by the Server DPC The Fourth WIM Meeting

  42. Outline • Problem Statement • Data Model • System Architecture • Tracking Moving Objects • NNC Search & Active Result • Distance between Moving Points • Conclusions • Proposals for Bachelor Projects The Fourth WIM Meeting

  43. System Architecture SERVER CLIENT NNC Request NNC Search Active Result User Query NNC Reply NNC Refresh Positioning Unit DB of Moving Points Position Update Client Position Road Network Road Network RN Update RN Input DB of Distances Visualization Result The Fourth WIM Meeting

  44. NNC Search • Searches for some number of DPs that are nearest to the QP • Application of the Best First Search in graphs • Extended with “reading” DPs from edges • During the search, all the DPs are fixed at the time when the search starts The Fourth WIM Meeting

  45. NNC Search • Searches for some number of DPs that are nearest to the QP • Application of the Best First Search in graphs • Extended with “reading” DPs from edges • During the search, all the DPs are fixed at the time when the search starts The Fourth WIM Meeting

  46. NNC Search • Searches for some number of DPs that are nearest to the QP • Application of the Best First Search in graphs • Extended with “reading” DPs from edges • During the search, all the DPs are fixed at the time when the search starts The Fourth WIM Meeting

  47. NNC Search • Searches for some number of DPs that are nearest to the QP • Application of the Best First Search in graphs • Extended with “reading” DPs from edges • During the search, all the DPs are fixed at the time when the search starts The Fourth WIM Meeting

  48. Active Result • Distance between QP and NNCs • Sorting NNCs with respect to the distance • Estimate of imprecision of NNCs • Expiration Number • Distance Limit The Fourth WIM Meeting

  49. Active Result • Distance between QP and NNCs • Sorting NNCs with respect to the distance • Estimate of imprecision of NNCs • Expiration Number • Distance Limit The Fourth WIM Meeting

  50. Active Result • Distance between QP and NNCs • Sorting NNCs with respect to the distance • Estimate of imprecision of NNCs • Expiration Number • Distance Limit The Fourth WIM Meeting