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

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

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

4. Road Network Data Model Road Network 2D  traffic regulations on intersections  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:

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

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

7. Transformation: Segments to Edges  A chain of segments ch = {s 1, …, s n }  An edge e = (v s, v e, w, l)  Co-edge relation coE  Components:  Weight is computed according to travel distance of paths of a chain: 70km/h 100km/h pth 1 pth 2 e1e1 e2e2  v s, v e corresponds to ends of chains  l corresponds to a sum of road distances of chain’s segments  ( e 1, e 2 )  coE if turn around on segments is allowed

8. Transformation: Connections To Vertices Single Vertex qp  no restrictions c  v  Mapping according to restrictions on movement on v :  any restrictions c  {v 1,…,v n }  {,…, } Connections qp Multiple Vertices qp X X  Components:  connection c =(p, mx)  vertex v  Semantics of vertex: can move to any outgoing edge from any ingoing edge

9. Transformation: Objects  Graph: dp G = (e, pos l, pos w, speed w, t)  Query point:  2D: qp 2D = (p, s)  pos l = RD(pth) + d(p k, qp)  pos w = TD (pth) + TD s (p k, qp) QP t1t1 t2t2 pth pos w pos l qp pkpk p1p1

10. Transformation: Objects DP lc 1  Graph: dp G = (e, pos l, pos w )  Data point:  2D: dp 2D = (prop={…}, loc={lc 1,lc 2,…})  Graph: dp G = (e, pos l, pos w, speed w, t)  Query point:  2D: qp 2D = (p, s)  One location to one (two) data point:  lc 1  dp 1 G, lc 2  dp 2 G, … Ph lc 2 QP t1t1 t2t2 pth pos w pos l qp  pos l = RD(pth) + d(p k, qp)  pos w = TD (pth) + TD s (p k, qp) pkpk p1p1

11. Outline  Problem Setting  Data Model and Transformation  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} A B

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

14. Scenario of Processing a New Query  User issues a query providing NNs, their number k, and Max Road Distance  Client searches for k NNs and validates the data set:  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. Position tracking Active result Quick selection k NN search Visual. Client Server Find not less than 3 open pharmacies around (157, 52) not further than 10 km Find 3 nearest open pharmacies within 10 km, User 4 open pharmacies, location of the query window Visualization of 3 pharmacies Validation  upon invalid data set reissues the query + Minimal Road Distance  upon valid data set maintains an active result and visualizes the result GPS

15. Scenario of Processing a Position Change  if Client has moved significantly from a point of last query to Server Quick selection Client Server User Visualization of 3 pharmacies  if Client has passed an intersection  if Client has changed speed or direction  Result of the query (a set of NNs) is adjusted according to the change of Clients GPS coordinates: Position tracking Active result k NN search Visual. GPS Validation 7 open pharmacies, location of the query window Find not less than 3 open pharmacies around (193, 53) not further than 10 km

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

17. X 10 X 11 Y 30 Y 31 1.825 1.8501.875 425 400 375 Grid Data Structure  A 2D map is covered by a grid.  Each data point in the map is associated with a cell.  Each cell has information about all data points within it.  A cell is accessed directly.

18. y5 y4 y3 y2 y1 x1x2x3x4x5x6 “Quick” Selection QPoint QWindow 3 QWindow 1 QWindow 2  Processing initial query:  Select data points from the cell of QPoint (QWindow 1 )  While ((NNCs < k) & (MRD not reached) & (there are unexplored cells)) {select NNCs from additional “ring”}

19. “Quick” Selection  A new QWindow is formed reusing already selected data. QWindow 2 QPoint QWindow 3 QPoint QWindow 1 QWindow 2 y5 y4 y3 y2 y1 x1x2x3x4x5x6  Only an update is sent to the Client:  additional data points  discarded data points  A query is received from Client  Processing subsequent query:  Processing initial query:  Select data points from the cell of QPoint (QWindow 1 )  While ((NNCs < k) & (MRD not reached) & (there are unexplored cells)) {select NNCs from additional “ring”}

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

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

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

23. NN Search Algorithms  was not visited  has the lowest travel distance  Next step – vertex that  Search in the graph is based on best-first search.  knnWOT turn-around is not allowed  knnWT turn-around is allowed 5 5 8 1 8 12 8 3 1 start root edge qp

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

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

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

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

28. Active Result for knnWT 1.5 -3.5 40 NULL CB dp1 [4] dp3 [14] dp2 [9] dp4 [4] SWAPPING qp [2.5] speed=1 alarms now now +1.5

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

30. 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)  Deletion of the data point from the NN list  perform NN search algorithm from the scratch  if edge was not traversed – do not insert a data point

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

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