ANIRBAN MONDAL IIS, University of Tokyo.

1. kNR-tree: A novel R-tree-based index for facilitating Spatial Window Queries on any krelations among N spatial relations in Mobile environments ANTHONY K. H. TUNG SOC, National University of Singapore MASARU KITSUREGAWA IIS, University of Tokyo. ANIRBAN MONDAL IIS, University of Tokyo. Contact E-mail: anirban@tkl.iis.u-tokyo.ac.jp

2. PRESENTATION OUTLINE INTRODUCTION PROBLEM FORMULATION QUERY PROCESSING The kNR-tree index PERFORMANCE STUDY RELATED WORK CONCLUSION AND FUTURE WORK

3. PRESENTATION OUTLINE INTRODUCTION PROBLEM FORMULATION QUERY PROCESSING The kNR-tree index PERFORMANCE STUDY RELATED WORK CONCLUSION AND FUTURE WORK

4. INTRODUCTION • Increasing popularity of mobile applications • Prevalence of spatial data and its applications Efficient processing of spatial queries in mobile environments This work focusses on the processing of spatial select queries on any k relations among N spatial relations in mobile environments  kNW queries

5. Motivation for kNW queries • A single client may be interested in objects from a number of different relations • Different clients may be interested in different numbers as well as different kinds of relations. • Mobile environments typically have multiple relations and user population demographics may vary considerably.

6. Examples of kNW queries • Find all bookshops, restaurants and car-parks which I will encounter nearby me during my next 10 minutes of travelling. • Find all bus stations and shopping centres which I will encounter nearby me during my next 15 minutes of travelling.

7. Examples of kNW queries • Find all bookshops, restaurants and car-parks which I will encounter nearby me during my next 10 minutes of travelling. • Find all bus stations and shopping centres which I will encounter nearby me during my next 15 minutes of travelling. kNW queries are beneficial in the real world.

8. MAIN CONTRIBUTIONS • Proposal of the kNR-tree, a single integrated novel R-tree-based structure for indexing objects from N different spatial relations. • kNR-tree facilitates kNW queries. • Processing of kNW queries in mobile environments • Differences from existing works • The window of the query is speculative (not known in advance) • the processing done by some of the base stations may not contribute to the final results. • We examine issues concerning objects from N different spatial relations.

9. PRESENTATION OUTLINE INTRODUCTION PROBLEM FORMULATION QUERY PROCESSING The kNR-tree index PERFORMANCE STUDY RELATED WORK CONCLUSION AND FUTURE WORK

10. PROBLEM FORMULATION • Given a set of base stations, each of which stores and manages the data (from N spatial relations) of mutually disjoint spatial regions and a set of mobile clients, the mobile client wishes to find the results of spatial window queries (on any k of the N relations) nearby himself within the duration of the next T time units.

11. THE CONTEXT • Each object is a point in space represented by its centroid. • Each object has a corresponding descriptor bitmap. • The descriptor bitmap for each object is exactly the same in terms of the entry positions of relation. • Tick entry positions as 1 if object has the relation, otherwise mark as 0. • Objects are static, but the clients who issue queries to the objects are mobile. • Alternative perspective of this problem: Indexing only one spatial relation with the type of the object as a scalar attribute of the space.

12. ILLUSTRATIVE EXAMPLE OF OBJECT BITMAPS

13. CLIENT QUERIES • Client queries are of the form (queryID, clientID, PIssue, SpeedMax, Qbitmap, Delta, Tau) • queryID is the unique query identifier • clientID is the unique client identifier • PIssue is the point of issue of the query • SpeedMax specifies client’s maximum speed. • Qbitmap is the query bitmap (an array of N bits) • Structure is exactly same in terms of entry positions of relations as object bitmap. • Delta quantifies the distance from client’s current location which M considers to be ‘nearby’ himself. • Tau indicates the duration of time (after issuing the query) during which the client would wish to receive the query results.

14. PRESENTATION OUTLINE INTRODUCTION PROBLEM FORMULATION QUERY PROCESSING The kNR-tree index PERFORMANCE STUDY RELATED WORK CONCLUSION AND FUTURE WORK

15. WINDOW QUERY PROCESSING IN MOBILE ENVIRONMENTS • We define Qcircle as a circle drawn with PIssue as centre and (Tau ×SpeedMax + Delta) as radius. • MBR of Qcircle is called QMBR. • Client cannotbe traveling at his maximum speed in all directions at once • QMBR is a speculative and conservative estimate of the query window • QMBR may intersect with the domains of multiple base stations

17. Case 1 • QMBR falls completely within one base station B’s domain • B processes QMBR on its own and sends results to client.

18. Case 2 • QMBR intersects with the domain of at least one base station other than B • B determines the set R of base stations with whose domains QMBR intersects. • For each member r of R, B determines the intersecting rectangular part between QMBR and r’s domain and sends the intersecting rectangular part to each r. • We refer to such intersecting rectangular parts as subQMBRs. • After processing its respective subQMBR, each r sends a COMPLETE message to indicate that it has completed processing its subQMBR.

19. PRESENTATION OUTLINE INTRODUCTION PROBLEM FORMULATION QUERY PROCESSING The kNR-tree index PERFORMANCE STUDY RELATED WORK CONCLUSION AND FUTURE WORK

20. The kNR-tree • kNR-tree is a single integrated Rtree-based structure for indexing objects from N spatial relations. • Non-leaf nodes of the kNR-tree contain entries of the form (ptr, mbr, Nbitmap) • ptr is a pointer to a child node in the kNR-tree • mbr is the MBR that covers all the MBRs in the child node. • Nbitmap consists of array of N entry bits, one for each spatial relation. • Leaf nodes of the kNR-tree contain entries of the form (oid, loc, Nbitmap) • oid is a pointer to an object in the database • loc is the location of the object.

21. Illustrative example of kNR-tree

22. Window query processing algorithm for kNR-tree

23. PRESENTATION OUTLINE INTRODUCTION PROBLEM FORMULATION QUERY PROCESSING The kNR-tree index PERFORMANCE STUDY RELATED WORK CONCLUSION AND FUTURE WORK

24. PERFORMANCE STUDY • Real dataset Greece Roads used for our experiments • The ‘Greece Roads’ dataset contains 23268 rectangles. • We computed the centroid of these rectangles to get 23268 points • Enlarging this dataset of points by translating and mapping the data. • Each of the base stations had more than 200000 points (objects) • Each point associated with at least one spatial relation • We used 16 base stations • kNR-tree used for indexing the points at each base station • We define the size of a query QSIZE as the percentage of a base station’s domain that a query covers. • Example: QSIZE = 20 implies that the query covers 20% of the area associated with the base station’s domain. • We used a fanout of 64 for the kNR-tree

25. Effect of variations in QSIZE

26. Effect of variations in k

27. PRESENTATION OUTLINE INTRODUCTION PROBLEM FORMULATION QUERY PROCESSING The kNR-tree index PERFORMANCE STUDY RELATED WORK CONCLUSION AND FUTURE WORK

28. RELATED WORK • Traditional R-tree-based indexes are not adequate for indexing mobile objects • Frequent updates  large number of node-splits and/or node-merges. • R-tree-based structures for mobile context • Time-parameterized R-tree (TPR-tree) • Spatio-Temporal R-tree (STR-tree) • Trajectory-Bundle tree (TB-tree) • Lazy Update R-tree (LUR-tree) • Multiversion 3D R-tree(MV3R-tree)

29. PRESENTATION OUTLINE INTRODUCTION PROBLEM FORMULATION QUERY PROCESSING The kNR-tree index PERFORMANCE STUDY RELATED WORK CONCLUSION AND FUTURE WORK

30. CONCLUSION AND FUTURE WORK • Summary • We have addressed efficient processing of kNW queries in mobile environments. • Our solution involves the use of our proposed kNR-tree. • A single integrated index for N spatial relations • Future Work • Detailed performance evaluation • Investigation of the effect of spatial density • Load-balancing among the base stations.