Irina Aleksandrova, Augustas Kligys, Laurynas Speičys

1. Computational Data Modeling and Queries for Location-Based Services in Road Networks Irina Aleksandrova, Augustas Kligys, Laurynas Speičys

2. Mobile User Ph Road Network Problem Setting Topic: • location-based services Applicationdomain: • road networks Scenario: • mobile users issue queries about stationary objects “Find the 3 nearest open pharmacies” Main issues: • data modeling • system architecture for query processing • algorithms, underlying computation of the query result

3. Outline Problem Setting Data Model and Transformation Querying System Architecture Query Processing Algorithms Future Work

4. Road Network 2D Road Network Data Model Road elements: Segments: • bi-directional, one-directional roads • separating lines • different properties on different directions of the single road (e.g., surface quality, speed limit) Connections: • traffic regulations on intersections

5. qp Ph Road Network Ph Ph 2D Objects’ Data Model Objects on the road network: Query point: • position Data points: • position • several locations • accessibility from different movement directions • properties

6. Transformation: the Idea Identify chains of segments • two segments meet • the same movement directions • the same properties Transform: • chains to edges • ending connections of chains to vertices 100km/h 70km/h 100km/h Transformation

7. 100km/h e1 e2 pth1 pth2 100km/h 70km/h Transformation: Segments to Edges Components: • A chain of segments ch = {s1, … , sn} • An edge e = (vs, ve, w, l) • Co-edge relation coE vs, ve corresponds to ends of chains l corresponds to a sum of road distances of chain’s segments Weight is computed according to travel distance of paths of a chain: (e1, e2)coE if turn around on segments is allowed

8. Transformation: Connections To Vertices Components: • connection c =(p, mx) • vertexv Semantics of vertex: can move to any outgoing edge from any ingoing edge Mapping according to restrictions on movement on v: • no restrictions c  v • any restrictions c  {v1,…,vn}{ ,…, } qp qp qp X X Single Vertex Multiple Vertices Connections

9. t2 qp qp posl t1 pth pk posw p1 QP Transformation: Objects Query point: • 2D: qp2D= (p, s) • Graph: dpG = (e , posl, posw, speedw, t) • posl = RD(pth) + d(pk, qp) • posw = TD (pth) + TDs (pk, qp)

10. Transformation: Objects Query point: t2 • 2D: qp2D= (p, s) qp qp posl • Graph: dpG = (e , posl, posw, speedw, t) t1 pth pk posw • posl = RD(pth) + d(pk, qp) p1 QP • posw = TD (pth) + TDs (pk, qp) Data point: • 2D: dp2D= (prop={…}, loc={lc1,lc2,…}) Ph lc1 • Graph: dpG = (e , posl , posw) lc2 • One location to one (two) data point: • lc1dp1G, lc2dp2G, … DP

11. Outline Problem Setting Data Model andTransformation Querying System Architecture Query Processing Algorithms Future Work

12. Querying Query: ”Find 2 nearest pharmacies” Problem: compute k-NN T=t1 Answer: {A,B} Problem: active result T=t2 Answer: {B,A} B A

13. Outline Problem Setting Data Model andTransformation Querying System Architecture Query Processing Algorithms Future Work

14. Find 3 nearest open pharmacies within 10 km, Find not less than 3 open pharmacies around (157, 52) not further than 10 km 4 open pharmacies, location of the query window Visualization of 3 pharmacies Scenario of Processing a New Query GPS Position tracking Quick selection Validation User Active result Visual. Server k NN search Client • User issues a query providing NNs, their number k, and Max Road Distance • Client issues a query to Server with user’s query and current position (x, y) • Server “quickly” selects l NNCs from an area around (x, y), 0l max NNCs in map. • Client searches for k NNs and validates the data set: • upon invalid data set reissues the query + Minimal Road Distance • upon valid data set maintains an active result and visualizes the result

15. Outline Problem Setting Data Model and Transformation Querying System Architecture Query Processing Algorithms • “Quick” Selection • Validation • k NN Search Algorithms • Handling Updates Future work

16. Grid Data Structure 375 A 2D map is covered by a grid. 400 Each data point in the map is associated with a cell. Each cell has information about all data points within it. 425 1.850 1.875 1.825 A cell is accessed directly. Y30 Y31 X10 X11

17. x1 x2 x3 x4 x5 x6 y1 y2 • While ((NNCs < k)& (MRD not reached) & (there are unexplored cells)) y3 QPoint QWindow1 y4 QWindow2 {select NNCs from additional “ring”} y5 QWindow3 “Quick” Selection Processing initial query: • Select data points from the cell of QPoint (QWindow1)

18. x1 x2 x3 x4 x5 x6 y1 y2 QPoint • While ((NNCs < k)& (MRD not reached) & (there are unexplored cells)) y3 QWindow1 y4 QWindow2 {select NNCs from additional “ring”} y5 QWindow3 • Only an update is sent to the Client: • additional data points • discarded data points QWindow2 “Quick” Selection Processing initial query: • Select data points from the cell of QPoint (QWindow1) Processing subsequent query: • A query is received from Client • A new QWindow is formed reusing already selected data. QPoint

19. Outline Problem Setting Data Model and Transformation Querying System Architecture Query Processing Algorithms • “Quick” Selection • Validation • k NN Search Algorithms • Handling Updates Future work

20. Frame validation: • solves data shortage problem • correct, if RD(qp, nnRDlast) < dist(qp,qw) • frame = normalized TD Validation Validation The result of the NNs list: • incorrect, if TD(qp, dp’) < TD (qp,dp)

21. Outline Problem Setting Data Model and Transformation Querying System Architecture Query Processing Algorithms • “Quick” Selection • Validation • k NN Search Algorithms • Handling Updates Future work

22. root edge qp NN Search Algorithms Search in the graph is based on best-first search. Next step – vertex that start 5 • was not visited • has the lowest travel distance 5 1 3 8 1 8 12 12 knnWOTturn-around is not allowed 8 knnWTturn-around is allowed

23. qp Algorithm knnWOT Search • scans the root edge and runs the best-first search from the end point of the root edge data points • data points on the root edge might appear twice in the NN list

24. qp Algorithm knnWOT Search • scans the root edge and runs the best-first search from the end point of the root edge • data points on the root edge might appear twice in the NN list Active result • discards data points from the NNlist that are behind the query point

25. dp4 dp3 dp2 co-qp dp1 dp3 Algorithm knnWT Search • Two search trees the first:considers the nearest data pointsthe query point is approaching to qp dp1 the second:considers the nearest data pointsthe query point is moving away • Merge results of both trees Active result • changes the order of the elements in the NN list

26. alarms -1 1.5 -3.5 speed=1 qp [1] Active Result for knnWT now now +1.5 dp1 dp3 dp2 dp4 B C [4] [14] [9] [4]

27. alarms -1 1.5 -3.5 SWAPPING alarms 4 0 NULL speed=1 qp [2.5] Active Result for knnWT now now +1.5 dp1 dp3 dp2 dp4 B C [4] [14] [9] [4]

28. Outline Problem Setting Data Model and Transformation Querying System Architecture Query Processing Algorithms • “Quick” Selection • Validation • k NN Search Algorithms • Handling Updates Future work

29. Deletion of the data point from the NN list • perform NN search algorithm from the scratch Handling Updates Insertion of the data point into the NN list • if the edge was already traversed (it is in the search tree) then insert a new data point into NN list (no other points are discarded) • if edge was not traversed – do not insert a data point

30. Outline Problem Setting Data Model and Transformation Querying System Architecture Query Processing Algorithms • “Quick” Selection • Validation • k NN Search Algorithms • Handling Updates Future work

31. Future Work Moving function for query point in 2D representation Predefined routes Using indexing in data selection accordingto the density of roads or objects Experiments