Active Nearest N eighbor Queries for Moving Objects

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