1. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Spatial Query Processing for High Resolutions Hans-Peter Kriegel, Martin Pfeifle, Marco Pötke, Thomas Seidl 8 th International DASFAA-Conference 26 - 28 March, 2003, Kyoto, Japan Database Group Institute for Computer Science University of Munich, Germany

2. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Outline of the Talk 1.) Introduction 2.) RI-Tree 3.) HRI-Approach 4.) Experimental Evaluation 5.) Conclusions

3. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich 1.) Introduction 2.) RI-Tree 3.) HRI-Approach 4.) Experimental Evaluation 5.) Conclusions  Spatial Databases  Voxelized Objects  High Resolutions Outline of the Talk

4. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Spatial Database Management Systems collision queries System Requirements:  Effectivity  Efficiency  Scalability  Concurrency Control  Recovery complex box queries spatialobjects Spatial Database Management Systems (based on extensible ORDBMS)

5. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Voxelized Spatial Objects triangulated objects voxel sequence 1.) linearization of the data space – grid-approximation – space filling curve interval sequence 2.) interval sequence – bottom-up or top-down – size-bound or error-bound

6. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Query Processing for High Resolutions Filter - Step Candidate Set for Application Specific Refinement Step Spatial - DB Refinement Step ORDBMSORDBMS CADCAD Result e.g. RI-Tree High Resolution HRI-Approach

7. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich 1.) Introduction 2.) RI-Tree 3.) HRI-Approach 4.) Experimental Evaluation 5.) Conclusions  Relational Interval Tree [VLDB 00] [VLDB 00]  Extensible Indexing Outline of the Talk

8. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Relational Interval Tree (RI-Tree) 3a3a 15 a 12 c 5c5c 15 a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 15 8 135713119 261014 412 A B C D 7b7b 1b1b 13 d  Foundation: Interval Tree [ Edelsbrunner 1980 ]

9. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich D  Foundation: Interval Tree [ Edelsbrunner 1980 ]  1. Idea: Virtualization of the Primary Structure 3a3a 15 a 12 c 5c5c 15 a 15 8 135713119 261014 412 7b7b 1b1b 13 d 15135713119 261014 412 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 12 h – 1 root = 2 h–1 Relational Interval Tree (RI-Tree)

10. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich  Foundation: Interval Tree [ Edelsbrunner 1980 ]  1. Idea: Virtualization of the Primary Structure  2. Idea: Managing of the Secondary Structure by 2 B + -trees nodelower 4 8 13 1 3 5 13 id bacdbacd nodeupper 4 8 13 7 12 15 13 id bcadbcad lowerIndexupperIndex Relational Interval Tree (RI-Tree) root = 2 h–1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 8 15135713119 261014 412 3a3a 15 a 12 c 5c5c 15 a 7b7b 1b1b 13 d A B C D

11. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich 1. Procedural Step 2. Declarative Step RI-Tree: Intersection Query

12. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich 1. Procedural Step 16 = root 24 = fork 25 28 26 20 22 23 2. Declarative Step – posting one single SQL-statement – number of I/O-accesses: O(h·log b n + r/b)  arithmetic traversal of the primary structure  collecting the visited nodes in transient tables  number of I/0-accesses: 0 select id from upperIndex i, :leftNodes left where i.node = left.node and i.upper >= :Q.lower union all select id from lowerIndex i, :rightNodes right where i.node = right.node and i.lower <= :Q.upper union all select id from upperIndex i where i.node between :Q.lower and :Q.upper 16 20 28 26 22-25 upper = 25 22 = lower query Q RI-Tree: Intersection Query

13. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich User-defined Index Structure [VLDB 00] [SSTD 01] Extensible Indexing Framework Object-relational interface for index maintenance and querying functions. Relational Implementation Mapping to built-in indexes (B + -trees); SQL-based query processing Physical Implementation Block-Manager, Caches, Locking, Logging, … User-defined Cost Model [SSDBM 02] Extensible Optimization Framework Object-relational interface for selectivity estimation and cost prediction functions. Relational Implementation Mapping to built-in statistics facilities; SQL-based evaluation of cost model Declarative Embedding Object-relational DML and DDL RI-Tree: Integration into an ORDBMS

14. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Outline of the Talk 1.) Introduction 2.) RI-Tree 3.) HRI-Approach 4.) Experimental Evaluation 5.) Conclusions  Grey Intervals  Storage of Grey Intervals in an Intervals in an ORDBMS ORDBMS  Intersection Queries based on based on Grey Intervals Grey Intervals

15. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Grey Intervals A voxelized “real-world” object Black object interval sequence (obtained from encoding voxels via a space filling curve) 082432404816 Grey object interval sequence (obtained from grouping black intervals together) O grey = ( id,   (2, 5), (7, 7) ,  (12, 12), (15, 15),(18, 18) ,  (22, 29) ,  (36, 36), (39, 39),(42, 42) ,  (46, 47)  )  (2, 5), (7, 7)  Grey Interval

16. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich +- bit-orientedapproachoffset-orientedapproach Storage of a Grey Object Interval Sequence 1 0 1 0 1 1 O (L)... 1 0 1 0 1 1... w1w1 w1w2w3w4w1w2w3w4 O (n * log L) w2w2 w3w3 w4w4 table schema GreyIntervals (id, intervalsequence) BLOB aggregated information H(I grey ), D(I grey ), G(I grey )

17. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Multi-Step Query Processing for Intersection Queries A 1 Q 1 A 3 Q 2 A 2 Q 1 B 3 Q 1 B 2 Q 1 C 1 Q 1 C 2 Q 1 C 2 Q 2 C 3 Q 2 D 1 Q 1 A 1 Q 1 A 3 Q 2 C 1 Q 1 DB Query Q A 1 Q 1 A 3 Q 2 A 2 Q 1 + B 3 Q 1 C 1 Q 1 C 2 Q 1 B 2 Q 1 ? result set Interval Index 1. filter step FAST GREY TEST 2. filter step BLOB TEST 3. filter step D1 Q1D1 Q1 A C B Q 1 Q 2 A 1 A 2 A 3 A B 1 B 2 B 3 B C 1 C 2 C 3 C 4 C D 1 D 2 D E 1 E... B 3 Q 1 + +

18. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich 2. filter step: FAST-GREY-TEST black interval + grey interval black interval covers the starting or end point of the grey interval grey interval + grey interval share the same starting or end point grey interval + grey interval number of white cells is smaller than the intersecting area... black interval + black interval L grey interval + other interval grey interval has only two black cells and the other interval is completely included in this interval grey interval + grey interval grey intervals have only two black cells and the intervals have no common starting or end point intersection no intersection long black interval + grey interval maximum gap of the grey interval smaller than the length of the black interval  intersection test based on the aggregated information of the grey intervals.

19. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich 3. filter step: BLOB-TEST  intersection test based on the examination of the black interval sequence... I2I2 I1I1 runtime analysis runtime analysis bit-oriented approach  finding the starting point A of the interlacing area  testing the L voxels L oLoL A O (1) O (L)

20. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich 3. filter step: BLOB-TEST... L I2I2 I1I1 w 1 w 2 w 3 w 4 w 5 w 6 w 7 w 8 A w6w6 w4w4 w7w7 n 1 = 8 n L1 = 1 n L2 = 3 runtime analysis runtime analysis offset-oriented approach  finding the starting point of the interlacing area  testing the n L1 resp. n L2 intervals O (log n 1 ) O (n L1 +n L2 )  intersection test based on the examination of the black interval sequence bit-oriented approach  finding the starting point A of the interlacing area  testing the L voxels O (1) O (L)

21. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich SQL-Statement SELECT candidates.id FROM (SELECT db.id AS id, table (AggInfos(db.intervalsequence, q.intervalsequence)) AS ctable FROM GreyIntervals db, :GreyQueryIntervals q WHERE intersects (hull(db.intervalsequence), hull(q.intervalsequence)) GROUP BY db.id )candidates WHERE EXISTS (SELECT 1 FROM GreyIntervals db, :GreyQueryIntervals q, candidates.ctable ctable WHERE db.rowid = ctable.dbrowid AND q.rowid = ctable.qrowid AND blobintersection (db.intervalsequence, q.intervalsequence) ) intersects (hull(db.intervalsequence), hull(q.intervalsequence)) table (AggInfos(db.intervalsequence, q.intervalsequence)) blobintersection (db.intervalsequence, q.intervalsequence)

22. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Outline of the Talk 1.) Introduction 2.) RI-Tree 3.) HRI-Approach 4.) Experimental Evaluation 5.) Conclusions

23. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Experimental Evaluation  Examination of the HRI approach based on different MAXGAP Parameters: 10 100 1,000 10,000 100,000 1,000,000  Comparison between the HRI approach and the spatial variant of the RI-tree [SSTD 01] CAR PLANE approx. 200 parts approx. 10.000 parts approx. 7 million intervals approx. 9 million intervals resolution: 33 bit (0.. 8.589.934.591) resolution: 42 bit (0.. 4.398.046.511.103)

24. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Experiments CAR  number of interval decreases with increasing MAXGAP - parameter  average interval length increases with increasing MAXGAP - parameter - Interval Distribution

25. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Experiments – Secondary Storage  With the HRI method we can improve the storage requirement by an order of magnitude. (RI-Tree)

26. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Experiments – Runtime for collision queries PLANE CAR

27. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Experiments – Runtime for collision queries PLANE CAR RI-tree huge part (PLANE) RI-tree: 316.5 s HRI: 2.2 s (Maxgap=10,000)

28. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Outline of the Talk 1.) Introduction 2.) RI-Tree 3.) HRI-Approach 4.) Experimental Evaluation 5.) Conclusions

29. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich What are the advantages of the HRI approach?  good secondary storage utilization Conclusions What is the HRI approach?  the HRI approach is a multi-step index structure suitable for spatial query processing for high resolutions  small main memory footprint  improved query response time behaviour

30. Kyoto, 03/26/03 Kyoto, 03/26/03 Martin Pfeifle, Database Group, University of Munich Any questions? ? ? ? ? ? ? ?