Motion Adaptive Indexing for Moving Continual Queries over Moving Objects

1. Motion Adaptive Indexing for Moving Continual Queries over Moving Objects CIKM, November, 2004 Bugra Gedik, KunLung Wu, Phlip Yu, Ling Liu

2. Outline • Introduction • The System Model • Evaluation of Range MCQs • Motion Sensitive Bounding Boxes • Predictive Query Results • Determining PQRs Using MSBs • Motion Adaptive Indexing (MAI) • Adaptive Parameter Selection • Experimental Results • Conclusion

3. Introduction (1/2) • Here are some examples of MCQs: • MCQ1 – “Give me the positions of those customers who are looking for taxi and are within 5 miles during next 20minutes.” • MCQ2 – “Give me the locations and names of the gas stations offering gasoline for less than $1.2 per gallon within 10miles, during the next half an hour.” • MCQ3 – “Give me the list of AAA vehicles that are currently on service call in 5 miles from my office location, during the next hour.”

4. Introduction (2/2) • There are two major types of MCQs － moving continual range queries and moving continual k-NN queries. • A moving continual range query has an associated moving object, called the focal object of the query. • In this paper, we use the concept of motion-sensitive bounding boxes (MSBs) to model moving objects and moving queries, and index them by MAI method. • We index less frequently changing object and query MSBs, where updates to the bounding boxes are needed only when objects and queries move across the boundaries of their boxes. • We also use predictive query results to optimistically pre-calculate query results.

5. The System Model (1/4) • First, we denote the set of moving or still objects as O, where O = Om∪ Os and Om∩ Os = empty set. Om denotes the set of moving objects and Os denotes the set of still objects. • Also, we denote the set of moving or still queries as Q, where Q = Qm∪ Qs and Qm∩ Qs = empty set. Qm denotes the set of moving continual queries and Qs denotes the set of static continual queries.

6. The System Model (2/4) • Moving Objects: < io, , , ap > • io : the unique object identifier • : the current location (px, py) of moving object • : the velocity vector (vx, vy) of the moving object • ap: a set of properties about the object • A still object can be modeled as a special case of moving objects where the velocity vector is set to zero.

7. The System Model (3/4) • Moving Queries: < iq, io, r, f > • iq: the unique query identifier. • io: the object identifier of the focal object of the query. • r : defines the shape of the spatial query region bound to the focal object of the query. • f : a Boolean predicate, called filter, defined over the properties (ap) of the target objects of the query. • A static spatial continual query:qs Qs, qs.io = null or qs.io Os

8. The System Model (4/4) • Motion Modeling and Update: • Motion Modeling – • It uses approximation for prediction. Moving objects only report their velocity vectors and position updates when their velocity vectors change significant enough. • The future position of the object at time t + Δt could be predicted as + Δt × . • Motion update generation – • If a moving object’s difference of motion update is larger than a specified threshold, say ΔD, the new motion function parameters are relayed to the server.

9. Evaluation of Range Query (1/13) • Motion Sensitive Bounding Boxes: • For all o Om : MSB (o) = Rect ( o. , o. + α(o) × o. )

10. Evaluation of Range Query (2/13) • Motion Sensitive Bounding Boxes: • For all q Qm : MSB (q) = Rect ( of. － q.r × sign (q. ), of. + β(q) × q. + q.r × sign (q. ))

11. Evaluation of Range Query (3/13) • Predictive Query Results: • Each object in the predictive query result has an associated time interval indicating time period in which the object is expected to be included in the query result. • Each entry in a predictive query result of takes the form < o, [ts, te] >. • We can calculate the time interval in which the object o is expected to be in the result set of query q by solving the following formula, where Dist (a, b) denotes the Euclidean distance between a and b:Dist ( of . + t × of . , o. + t × o. ) ≦ qm.r

12. Evaluation of Range Query (4/13) • Issues of Predictive Query Results : • Prediction?For each moving query, should we perform prediction on all moving objects? • Invalidation?When and how to update the predictive results?

13. Evaluation of Range Query (5/13) • Determining PQRs Using MSBs:

14. Evaluation of Range Query (6/13) • Motion Adaptive Indexing: • Processing Moving Queries • The Scan Algorithms

15. Evaluation of Range Query (7/13) • MAI (Processing Moving Queries): • Two MSB indexes are built: and . • Two tables are maintained: MOT and MQT.

16. Evaluation of Range Query (8/13) • MAI (The Scan Algorithms):Two scans will be performed. • MOT Scan: • Check whether the associated object of the entry has invalidated its MSB or changed its motion function. • Update if upper case happens. • Search , update query results by MSBold and MSBnew. • MQT Scan.

17. Evaluation of Range Query (9/13) • Adaptive Parameter Selection: • ※ There are two important characteristics of object motions: • the speed of the object; • the period of constant motion of the object, Pcm. • For instance, for a query whose focal object changes its motion function frequently, it may not be a good idea to perform too much prediction.

18. Evaluation of Range Query (10/13) • Adaptive Parameter Selection:Analytical Model for IO Estimation ~ Amo ≒ ( α × | v |／ )2 Amq ≒ ( β × | v |／ + 2 × Rmq )2 Ao ≒ Amo × Nmo／No ......... (assume still objects’ MSB = 0) Aq ≒ × ( Amq × Nmq + × (Nq – Nmq)) Assuming that the x and y components of the velocity vector are equal.

19. Evaluation of Range Query (11/13) • Example:

20. Nmot ≒ + － × Evaluation of Range Query (12/13) • Adaptive Parameter Selection: Analytical Model for IO Estimation ~ If Ps／Pcm < 1, that is, only some of the moving objects will cause velocity change events, then, ≒ Nmo × min (1, ) ≒ × ≒ min ( , 1) × Nmo ≒ min ( , 1) × Nmq Nmot ≒ + － ×

21. Evaluation of Range Query (13/13) • Adaptive Parameter Selection:Analytical Model for IO Estimation ~ Finally, we have a total IO cost for the periodic scan, Cio, can then be calculated as follows:Cio = Nmot × ( + 2 × ) + Nmqt × ( + ) where : node IO cost during processing an object table entry for updating the : node IO cost during processing an object table entry for searching the : node IO cost during processing a query table entry for updating the : node IO cost during processing a query table entry for searching the

22. Experimental Result (1/6) • System parameters Besides, in this paper, they build a off-line computed αβTable, which gives the optimal pair (α, β) to a object and its associated query.

23. Experimental Result (2/6) • Performance Comparison: BF: Brute ForceOI : Object-only IndexingQI : Query-only IndexingOQI: Object and Query IndexingMAI: Motion Adaptive IndexingOIB: Object Indexing with MSBs Scan Period

24. Experimental Result (3/6) • Performance Comparison (cont.): BF: Brute ForceOI : Object-only IndexingQI : Query-only IndexingOQI: Object and Query IndexingMAI: Motion Adaptive IndexingOIB: Object Indexing with MSBs

25. Experimental Result (4/6) • Effect of Adaptive Parameter Selection: Class A: moving slow, but change their motion function frequently. Class B: moving and change their motion function as default settings. Class C: moving fast, but seldom change their motion function. Conclusion: It’s expensive to deal with Class A and Class C.

26. Experimental Result (5/6) • Scalability :Effect of query range and moving object percentage on performance ~

27. Experimental Result (6/6) • Scalability (cont.): Effect of number of objects on performance~

28. Conclusion • This paper presented a system and a motion-adaptive indexing scheme for efficient processing of moving continual queries over moving objects.