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Spatial Query Processing
for High Resolutions
Hans-Peter Kriegel, Martin Pfeifle,
Marco Pötke, Thomas Seidl
Database Group
Institute for Computer Science
University of Munich, Germany
Martin Pfeifle, Database Group, University of Munich
8th International DASFAA-Conference
26 - 28 March, 2003, Kyoto, Japan
Kyoto, 03/26/03
Outline of the Talk
1.) Introduction
2.) RI-Tree
3.) HRI-Approach
4.) Experimental Evaluation
5.) Conclusions
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
Outline of the Talk
1.) Introduction
 Spatial Databases
 Voxelized Objects
2.) RI-Tree
 High Resolutions
3.) HRI-Approach
4.) Experimental Evaluation
5.) Conclusions
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
Spatial Database Management Systems
System Requirements:
box queries
 Effectivity
collision queries
 Efficiency
complex
spatial
objects
 Scalability
 Concurrency Control
 Recovery
Spatial Database
Management Systems
(based on extensible ORDBMS)
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
Voxelized Spatial Objects
1.) linearization of the
data space
– grid-approximation
– space filling curve
2.) interval sequence
– bottom-up or top-down
– size-bound or error-bound
triangulated objects
voxel sequence
interval sequence
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
Query Processing for High Resolutions
O
R
D
B
M
S
C
A
D
Martin Pfeifle, Database Group, University of Munich
High Resolution
Spatial - DB
Filter - Step
e.g. RI-Tree
HRI-Approach
Candidate Set for
Application Specific
Refinement Step
Refinement
Step
Result
Kyoto, 03/26/03
Outline of the Talk
1.) Introduction
 Relational Interval Tree
[VLDB 00]
2.) RI-Tree
 Extensible Indexing
3.) HRI-Approach
4.) Experimental Evaluation
5.) Conclusions
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
Relational Interval Tree (RI-Tree)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
A
B
C
D
8
4
1b
2
1
3
7b
6
5
3a
15ca
12
5c
15a
7
12
10
9
14
11
13
15
13d 13d
 Foundation: Interval Tree [Edelsbrunner 1980]
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
Relational Interval Tree (RI-Tree)
1
2
3
4
5
6
7
8
9
10
11
12
13
root = 2h–1
14
15
D
8
4
1b
2
1
3
7b
6
5
3a
15ca
12
5c
15a
7
12
10
9
14
11
13
13d 13d
1
15
2h – 1
 Foundation: Interval Tree [Edelsbrunner 1980]
 1. Idea: Virtualization of the Primary Structure
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
Relational Interval Tree (RI-Tree)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
A
B
C
D
root = 2h–1
8
4
1b
2
1
3
7b
6
5
3a
15ca
12
5c
15a
7
12
10
9
14
11
13
15
13d 13d
 Foundation: Interval Tree [Edelsbrunner 1980]
 1. Idea: Virtualization of the Primary Structure
 2. Idea: Managing of the Secondary Structure by 2 B+-trees
node lower id
4
8
8
13
1
3
5
13
b
a
c
d
lowerIndex
Martin Pfeifle, Database Group, University of Munich
node upper id
4
8
8
13
7
12
15
13
b
c
a
d
upperIndex
Kyoto, 03/26/03
RI-Tree: Intersection Query
1. Procedural Step
2. Declarative Step
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
RI-Tree: Intersection Query
1. Procedural Step
query Q
22 = lower
upper = 25
 arithmetic traversal
of the primary structure
 collecting the visited nodes
in transient tables
 number of I/0-accesses:
0
16 = root
24 = fork
20
28
26
22
23 25
16 20
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
Martin Pfeifle, Database Group, University of Munich
28 26
22-25
2. Declarative Step
– posting one single
SQL-statement
– number of I/O-accesses:
O(h·logbn + r/b)
Kyoto, 03/26/03
RI-Tree: Integration into an ORDBMS
Declarative Embedding
Object-relational DML and DDL
Extensible Indexing Framework
Extensible Optimization Framework
Object-relational interface for index
maintenance and querying functions.
Object-relational interface for selectivity
estimation and cost prediction functions.
User-defined Index Structure
[VLDB 00] [SSTD 01]
User-defined Cost Model
[SSDBM 02]
Relational Implementation
Relational Implementation
Mapping to built-in indexes (B+-trees);
SQL-based query processing
Mapping to built-in statistics facilities;
SQL-based evaluation of cost model
Physical Implementation
Block-Manager, Caches, Locking, Logging, …
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
Outline of the Talk
1.) Introduction
 Grey Intervals
2.) RI-Tree
 Storage of Grey
Intervals in an
ORDBMS
3.) HRI-Approach
4.) Experimental Evaluation
 Intersection Queries
based on
Grey Intervals
5.) Conclusions
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
Grey Intervals
A voxelized “real-world” object
Black object interval sequence (obtained from encoding voxels via a space filling curve)
0
8
16
24
32
40
48
Grey object interval sequence (obtained from grouping black intervals together)
Ogrey = ( id,  (2, 5), (7, 7)
7), (12, 12), (15, 15),(18, 18), (22, 29), (36, 36), (39, 39),(42, 42), (46, 47))
Grey Interval
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
Storage of a Grey Object Interval Sequence
table schema GreyIntervals (id, intervalsequence)
BLOB
aggregated information
H(Igrey), D(Igrey), G(Igrey)
+
L
2  (n  1)  log2 L 
-
bit-oriented
approach
offset-oriented
approach
...
...
1
0
1
0
1
...
...
w
1
1
1 0 1 0 1 1
O (L)
Martin Pfeifle, Database Group, University of Munich
w2 w
w 1w 2w 3w 4
3
w
4
O (n * log L)
Kyoto, 03/26/03
Multi-Step Query Processing
for Intersection Queries
result
set
DB
A
C
B
A1
A2 A3
B1 B2 B3
C1 C2 C3 C4
D1
D2
...
A
B
C
D
A11 Q11
A
A3 Q
Q
A
3 22
A22 Q11
A
E1 E
Interval
Index
+
1. filter step
Q1 Q2
Query Q
B3 Q1
B2 Q1
C
C11 Q1
C
Q21 Q1
C2
Q1
C2
Q
D12 Q1
C3
Q2
D1
Martin Pfeifle, Database Group, University
Q1of Munich
+
FAST
GREY
TEST
A1 Q1
A3 Q2
?
2. filter step
B3 Q1
B2 Q1
C1 Q1
BLOB
TEST
+
3. filter step
Kyoto, 03/26/03
2. filter step: FAST-GREY-TEST
 intersection test based on the
aggregated information of the grey intervals.
...
...
black interval + black interval
intersection
black interval + grey interval
black interval covers the starting or end point of the grey interval
long black interval + grey interval
maximum gap of the grey interval smaller than the length of the black interval
grey interval + grey interval
share the same starting or end point
grey interval + grey interval
no
intersection
L
number of white cells is smaller than the intersecting area
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
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
3. filter step: BLOB-TEST
 intersection test based on the
examination of the black interval sequence
oL
...
A
L
...
I1
I2
runtime analysis
bit-oriented approach
 finding the starting point A
of the interlacing area
O (1)
 testing the
L voxels
O (L)
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
3. filter step: BLOB-TEST
 intersection test based on the
examination of the black interval sequence
A
...
w77
w1 w2 w3 w44 w5 w
w66 w
L
w8
...
I1
n1 = 8 nL1 = 1
nL2 = 3
I2
runtime analysis
bit-oriented approach
offset-oriented approach
 finding the starting point A
of the interlacing area
O (1)
 finding the starting point
of the interlacing area O (log n1)
 testing the
L voxels
 testing the
nL1 resp. nL2 intervals
O (L)
Martin Pfeifle, Database Group, University of Munich
O (nL1+nL2)
Kyoto, 03/26/03
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)
)
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
Outline of the Talk
1.) Introduction
2.) RI-Tree
3.) HRI-Approach
4.) Experimental Evaluation
5.) Conclusions
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
Experimental Evaluation
CAR
approx. 200 parts
approx. 7 million intervals
resolution: 33 bit (0 .. 8.589.934.591)
PLANE
approx. 10.000 parts
approx. 9 million intervals
resolution: 42 bit (0 .. 4.398.046.511.103)
 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]
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
Experiments - Interval Distribution
10000000
M=10^1
1000000
M=10^2
100000
M=10^3
10000
M=10^4
1000
M=10^5
100
M=10^6
10
1
26
21
44
20
97
15
2
16
77
72
16
40
96
32
76
8
51
2
64
Interval-Length
8
1
number of intervals
CAR
M=0 (RI-Tree)
 number of interval decreases
with increasing MAXGAP - parameter
 average interval length increases
with increasing MAXGAP - parameter
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
number of blocks
[x1000]
Experiments – Secondary Storage
160
140
120
100
80
60
40
20
0
PLANE
indexes
table
0
MAXGAP
1000000
1000
(RI-Tree)
With the HRI method we can improve the storage requirement
by an order of magnitude.
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
time [sec]
CAR
Experiments – Runtime for collision queries
3.FilterStep
2.FilterStep
50
40
30
20
10
0
1.FilterStep
10
100
time [sec]
PLANE
0.8
1000
10000
100000
Maxgap
1000000
3.FilterStep
0.6
2.FilterStep
0.4
1.FilterStep
0.2
0.0
10
100
1000
10000
Martin Pfeifle, Database Group, University of Munich
100000
Maxgap
1000000
Kyoto, 03/26/03
time [sec]
CAR
Experiments – Runtime for collision queries
3.FilterStep
2.FilterStep
50
40
30
20
10
0
1.FilterStep
10
100
time [sec]
PLANE
0.8
1000
10000
100000
Maxgap
1000000
RI-tree
RI-tree: 316.5 s
HRI:
2.2 s
(Maxgap=10,000)
3.FilterStep
0.6
2.FilterStep
0.4
1.FilterStep
huge part
(PLANE)
0.2
0.0
10
100
1000
10000
Martin Pfeifle, Database Group, University of Munich
100000
Maxgap
1000000
RI-tree
Kyoto, 03/26/03
Outline of the Talk
1.) Introduction
2.) RI-Tree
3.) HRI-Approach
4.) Experimental Evaluation
5.) Conclusions
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
Conclusions
What is the HRI approach?
 the HRI approach is a multi-step index structure
suitable for spatial query processing for high resolutions
What are the advantages of the HRI approach?
 good secondary storage utilization
 small main memory footprint
 improved query response time behaviour
Martin Pfeifle, Database Group, University of Munich
Kyoto, 03/26/03
?
?
?
?
Any questions?
?
Martin Pfeifle, Database Group, University of Munich
?
?
Kyoto, 03/26/03