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A new approach on indexing mobile objects on the plane

A new approach on indexing mobile objects on the plane. S. Sioutas. K. Tsakalidis. K. Tsichlas. C. Makris. Y. Manolopoulos. John Greene CSUID: 2475507. Outline. Introduction Presentation of the most basic methods Definitions and problem description

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A new approach on indexing mobile objects on the plane

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  1. A new approach on indexing mobile objects on the plane S. Sioutas K. Tsakalidis K. Tsichlas C. Makris Y. Manolopoulos John Greene CSUID: 2475507

  2. Outline • Introduction • Presentation of the most basic methods • Definitions and problem description • Indexing mobile objects in 2 dimensions • The access methods • Experimental evaluation

  3. Introduction • Focus on mobile objects in two dimensions • Two basic approaches • Representations include: • R-trees & quadtrees • Geometric duality • Index native dimensional space

  4. Introduction • Examples include: • Intelligent transportation systems • Cellular communications • Meteorology monitoring

  5. Literature Survey – presentation of the most basic methods • Geometric Duality Transformation • B+ Trees • Partition Trees • TPR*-Trees • STRIPES

  6. Definitions & Problem Description • Consider a database: • Records position • Moving objects • Finite terrain

  7. Definitions & Description • Velocity bounded by [Umin,Umax] • Pz(t0) = [X(t),y(t)] – initial position of z • U = [ux,uy] – velocity vector • For t > t0, Pz(t) = [x(t),y(t)] = [x0+ux(t-t0), y0+uy(t-t0)]

  8. Indexing Mobile Objects in Two Dimensions • Need to simplify • Hough-X Transform • Map y(t) = ut + a to a single point • One axis represents slope (velocity) • Other axis represents intercept (a) • Query becomes: [(Umin,Umax),(y1q-t1qumax,y2q-t2qumin)]

  9. Indexing Mobile Objects in Two Dimensions

  10. Indexing Mobile Objects in Two Dimensions • Hough-Y Transform • Rewrite the equation y = ut+a as t = 1/uy - a/u • Coordinates (b,w) • b = - a/u • W = 1/u • Query becomes:

  11. Indexing Mobile Objects in Two Dimensions • Motions with small velocities in the Hough-Y approach are mapped into dual points (b,n) having large n coordinates (n=1/u) • By storing the Hough-Y dual points in an index structure such as an R* -tree, MBR's with large extents are introduced, and the performance is severely affected. • By using a Hough-X for the small velocities' partition, this effect is eliminated • The query area in Hough-X plane is enlarged by the area EHough-X =E1Hough-X + E2Hough-X • and in Hough-Y plane by EHough-Y =E1Hough-Y + E2Hough-Y • QHough-X = actual area of the simplex query in Hough-X plane • QHough-Y = actual area of the simplex query in Hough-Y plane • Thus, the overall solution proposes the choice of that transformation which minimizes the criterion...

  12. Indexing Mobile Objects in Two Dimensions Build the index • Decompose the 2D motion into two 1D motions on the (t,x) and (t,y) planes. • For each projection, build the corresponding index. Partition objects based on velocity • Small velocity => stored using Hough-X transform • Others => stored using Hough-Y transform • Motion information about the other projection is also included.

  13. Indexing Mobile Objects in Two Dimensions Outline for algorithm of 2D query: • Decompose the query into two 1-d queries, for the (t,x) and (t,y) projection • For each projection get the dual - simplex query • For each projection calculate the criterion c and choose the one (say p) that minimizes • Search in projection p the Hough-X or Hough-Y partition • Perform a refinement or filtering step “on the fly” by using the whole motion information. Thus, the result set contains only the objects that satisfy the query

  14. Indexing Mobile Objects in Two Dimensions Innovative Contributions Based on: • the use of the Lazy B-tree instead of the B+ tree when handling queries with the Hough-Y transform • the employment of a new index that outperforms partition trees in handling polygon queries with the Hough-X transform.

  15. The access methods

  16. The access methods Lazy B-trees • L and Li, where 1 ≤ i ≤ O(logN) • Remaining operations guided by the global rebalancing lemma • Each bucket assigned criticality • Update buckets with largest criticality • Every update performed incrementally

  17. Experimental Results • Taken rom LA spatial dataset • Wanted all objects moving in space of 100×100km • Page size 1Kb • Key length 8 bytes, pointer 4 bytes • For simplicity, all objects are stored using the Hough-Y dual transform.

  18. 26.56 times faster than STRIPES! Experimental results • Performance degrades as query rectangle length grows from 100 to 1000

  19. Experimental results

  20. Experimental results Impact of increased velocity

  21. Experimental results Impact of reduced time interval

  22. Experimental results Impact of increased time interval

  23. Experimental results Average Cost

  24. Experimental results Gigantic Data Sets

  25. Questions?

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