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Spatial Databases and Spatial Indexing Techniques

Timos Sellis

Computer Science Division Department of Electrical and Computer

Engineering National Technical University of Athens

Zografou 15773, GREECE

Tel: +30-1-772-1601 FAX: +30-1-772-1659

e-mail: [email protected]

Spatial Database Systems Timos Sellis

1

Spatial Databases and Spatial Indexing Techniques

Timos SellisNational Technical University of Athens

e-mail: [email protected]

Aalborg, June 1998

Spatial Database Systems 1

Outline

• Data Models• Algebra• Query Languages• Data Structures• Query Processing and Optimization• System Architecture• Open Research Issues


2


Introduction : Spatial Database Management Systems (SDBMS)

QUESTION“What is a Spatial Database Management System ?”

ANSWER• SDBMS is a DBMS

• It offers spatial data types in its data model and query language• support of spatial relationships / properties / operations

• It supports spatial data types in its implementation• efficient indexing and retrieval • support of spatial selection / join


Applications of SDBMS

Traditional GIS applications

• Socio-Economic applications• Urban planning• Route optimization, market analysis

• Environmental applications• Fire or Pollution Monitoring

• Administrative applications• Public networks administration • Vehicle navigation


3


Applications of SDBMS (cont'd)

Novel applications

• Image and Multimedia databases• shape configuration and similarity issues

• medical databases

• Time-series databases• management of time intervals

• Traditional DBMS• data warehouses


SDBMS Requirements

• Manipulation of very large amounts of data e.g. terabytes of data per day from satellite images

• Data distinctionspatial and non-spatial (alphanumeric) data

• Complex spatial relationships and operationstopological, directional, metric relationships,

spatial join operation


4


SDBMS Requirements (cont'd)

• Complex spatial relationships(topological, directional,metric)• “Find all cities adjacent to a river”• “Find all dark shapes left to the heart”• “Find the 5 closest hospitals with respect to a given location”

• Spatial join: An expensive operation• “Find the 5 closest hospitals with respect to any highway”


SDBMS Issues of Interest

• Data Models• Algebras• Query Languages• Data Structures• System Architectures


5


Spatial Data Models

• Two main approaches for spatial representation

• raster model(image-based partition of space)

• vector model(object-based partition of space)

R

RRR

R

RRR

R

H

X-AxisY

-Axi

s

River

House


Raster Model

• RASTER MODEL

subdivision of space into cells of regular size and shape(i.e., regular tessellation)

square triangular hexagonal


6


Raster Model (cont'd)

• RASTER MODEL (cont'd)

• each cell is assigned the value of the attribute it represents• each cell in a raster file is assigned only one value• different attributes are stored in separate files (layers)


Raster Model (cont'd)

• RASTER MODEL (cont'd)

Example:

land cover land layerArea water resources water layer

topography topography layer


7


Vector Model

• VECTOR MODEL

• subdivision of the space based on geographic features position (i.e., irregular tessellation)

• features are represented by (2-D space): • Points (x,y)• Lines (x1,y1, x2,y2, ..., xn,yn)• Regions (x1,y1, ..., xn,yn, x1,y1)

... referred to a common coordinate system (X,Y)


Vector Model (cont'd)

• VECTOR MODEL (cont'd)

• Layer-based model:features organised into separate layers (files) based on their properties

• Feature-based model:features organised into one layer (file) and characterised by a code (closer to O-

O approach)


8


Spatial Algebra

Spatial operations

• Local• information retrieval (e.g. point-in-polygon

query)• classification and recoding• measurement (e.g. area, perimeter)• polygon overlay / spatial join


Spatial Algebra (cont'd)

Spatial operations (cont'd)

• Zonal• spatial selection

• Focal• proximity determination • (e.g. Voronoi diagrams)• interpolation


9


Spatial Query Languages

• Database query languages are the tools that end-users most often use to interact with a spatial database system.

• Such a language should be:• powerful enough to express a query involving both spatial and

non-spatial components• simple enough to use effectively as an interface between user

and system


Spatial Query Languages (cont'd)

Basic queries:Spatial selection• Find all rivers within a specified area • Find all cities within a 100Km distance from Athens

Spatial join• Find all cities within a 10Km distance from any shoreline.

Spatial Query Languages• New languages ‘from-the-scratch’ (e.g. GEO-SAL [SH91])• Extensions of well-known languages such as SQL, QUEL (e.g. GEOQL

[OSM89], PSQL [RFS88])


10


PSQL

• Pictorial Structured Query Language (PSQL) [RFS88]:

An SQL extension, which supports:• spatial entity types (point, segment, region), and• spatial operators

• topological (e.g. overlaps, covers, within)• directional (e.g. north_of, south_of)


PSQL (cont'd)

PSQL Syntax:SELECT < attribute-list >FROM < relation-list > ON < picture-list > WHERE < condition >

Example:SELECT state, state_region, population_densityFROM states, cities ON us_map WHERE state_region overlap circle (location, 1500) AND city_name = “Washington, D.C.”


11


Requirements

• Specialized data structures are necessary, for performance, uniformity, etc.

• Point- and non-point objects need to be efficiently indexed and retrieved

• Support of several spatial relationships is necessary

Spatial Data Structures


Examples

• Raster Model:• Quadtrees

• Vector Model:• K-D-B-trees, Quadtrees, Grid Files (for points), • R-trees and variations (for non-point objects)

Spatial Data Structures (cont'd)


12


Data Structures, Raster Model

• Quadtrees [Sam84]

Data set

0 1

20322

21

23

Representation

0 1 2 3

root

20 21 22 23

Quadtree


Data Structures, Vector Model

• Using approximations instead of the exact geometry of shapese.g. the Minimum Bounding Rectangle (MBR)

Example:

GRIT

SPPO

FR

IR

UK

IC

NOFI

SW

DE

GENL

BE LU

PL

CZ

RO

BU

ALYU

CH

AUHU


13


Data Structures, Vector Model (cont'd)

• Two-step query processing

• Filter step: based on objects’ approximations to output the candidate set

• Refinement step: comparison of actual objects’ geometric shapes to output the answer set


Data Structures, Vector Model(cont'd)

• Several indexing methods (a survey in [GG95])

• R-tree family: the most popular onese.g. R- [Gut84], R+- [SRF87], R*- [BKSS90] etc.

• Numerous applications (“trees have grown everywhere” [SRF97])Multimedia / medical / time-series databases, data warehouses, ...


14


R-Trees

An example of R-trees

DE

F

H I

K

J

M

N L

GA

B

C

A B C

D E F G H I J K L M N


R-Trees (cont'd)

An example of R-trees

DE

F

H I

K

J

M

N L

GA

B

C

A B C

D E F G H I J K L M Npoint query

range query


15

VLDB 97 28

Packed R-trees

• Problems with random insertions• Goal:

• minimal coverage of leaf nodes• minimal overlap of intermediate nodes

• Sorting & packing of spatial objects improves search & space performance by 1-2 orders of magnitude

• Starting point for R+-trees, R*-trees, Hilbert R-trees, &Cubetrees

VLDB 97 29

R+-trees

B

I

K

J

A

C

DE

F

H

M

NL

G

P

A B C

D E F G I J K L M N

P

G H

May add more levels to the tree.....but it is faster


16

VLDB 97 30

What has been done since 1987?

• Lots of other improvements and extensions to the basic structure (R*-tree, Hilbert R-tree, TV-Tree, P- and JP-Tree, and many more)

• Commercial systems are incorporating them• Has given rise to lots of interesting other research

• More packing algorithms• Spatial joins• Direction queries• Parallelization• Nearest-neighbor queries• Analysis of algorithms and structures

VLDB 97 31

Nearest Neighbor Searching

downward pruning

MINMAXDIST

MINDIST

P

NN is there

M11

M12

M13

MBR1

M21 M22

MBR2


17

VLDB 97 32

Analysis of R-trees

• Uniformity assumption

• BUT: pessimistic + unrealistic

• Solution: FRACTALS - What is the fractal dimension?• ≈ “intrinsic” dimensionality

• Nominal dimension = 2• “Intrinsic” dimension = 1

VLDB 97 33

Analysis of R-trees

Non-integer fractal dimensions• e.g. sierpinski triangle

• fractal dimension = log3/log2 = 1.59


18

VLDB 97 34

Analysis of R-trees

Are real data sets fractal?

• Coastlines ( fd = 1.1 - 1.58 - e.g. Norway !)• Mamalian brain surface (2.7)• Cardiovascular system (3!)• Stock prices (1.5)• “Montgomery County” (~1.7)

VLDB 97 35

Analysis of R-trees

End result: Great accuracy in estimations !

• Range queries in R-trees (<10% error versus ~20% of uniformity)

• Spatial joins (<10% vs 100%)• Nearest-neighbors (good bounds)


19

VLDB 97 36

What was the influence?

• More than a decade of very active and intense research and development

• “Reaching out” to other areas, e.g.• active database systems• indexing multimedia databases by content • supporting OLAP and DataCube processing • indexing time sequences• data mining and clustering

VLDB 97 37

C D

B

7

8

18

12

A

Θ

(10,50)

F

Time

FE

D

A

10 13 17 20 24 28È

C

B

30

spatial layout temporal layout

queries spatial - temporal - spatio-temporal

Indexing Multimedia Presentations


20

VLDB 97 38

OLAP - Cubetrees

Table R(A,B,C,Q)

Relation tuple

groupby(A,C)

groupby(B)

groupby(A,B)

groupby(B,C)

groupby(A)

groupby(C)

groupby(none)relation tuples: points in the N-d spacegroupby projections: also pointspoint data is very efficient for multidimensional indexing

C

T(a,b,c,q)

(a,0,0,q)

(a,b,0,q)

(a,0,c,q)

(0,b,0,q)

(a,b,0,q)

T (a,b,c,q)

(a,0,0,q)

(a,0,c,q)

A

B

(0,b,0,q)

(0,b,c,q)

(0,0,c,q)

(0,b,c,q)

0

(0,0,c,q)

VLDB 97 39

Packing & Sort Order ofCubetrees

} these groupbys dispersed (on different pages)

For a chosen sort order : A,B,CB

A

C

Cubetrees are packed and compressed from N-d to lower dimensions Sort order is used for merging during incremental bulk updates

}well clustered groupbys (on the same or consecutive pages)


21

VLDB 97 40

Cubetrees for OLAP Queries

• Very fast OLAP queries (2-3 orders of magnitude)

• Minimal space overhead (less than 15%)

• Efficient bulk updates (6 GB per hour on a single processor/single disk)

• Scalable solution (merge packing)


Query Processing & Optimization

Query Processing

Examples of queries• Point / range queries• Direction, topological, distance queries• k- Nearest neighbor queries• Spatial join queries (join based on any spatial operator)


22



Query Processing (cont'd)

HOW?• by using specialized indexing methodsor• by making appropriate transformations in order to use methods

for point / range queries



Query Processing (cont'd)

Example“Find all countries northeast

of Switzerland”

The transformation is not always trivial !


23



Query Optimization

• Heuristic rulesnot so clear as those for traditional DBMS

• Cost Estimatesmainly based on uniformity assumption (e.g. [FSR87])


• Extending traditional DBMS architecture by introducing:

• new data models and query languages • specialized data structures and access methods• new techniques for query optimization

• GUIs for input / output

System Architecture


24


• Alternative strategies to implement an SDBMS:

• Hybrid system: introduce a specialized software (for storage and analysis of spatial data) within a standard DBMS

• Extensible DBMS: develop appropriate an integrated architecture based on extensible DBMS facilities

System Architecture


• Hybrid System

Examples: ARC/INFO [Mor89], SAND [AS91]

ATTRIBUTEDATABASE

SPATIALDATABASE

SPECIALIZED ‘SPATIAL’ S/W

S/WTO MANAGE

SPATIAL DATA

STANDARD DBMSTO MANAGE

NON-SPATIAL ‘ATTRIBUTE’ DATA

System Architecture (cont'd)


25


• Extensible DBMS

Examples: PROBE [OM88], Gral [Gut89], DASDBS [SPSW90]

EXTENSIONSTO ACCOMMODATE

SPATIAL DATASPATIAL ANDATTRIBUTEDATABASE

EXTENSIBLEDBMS

System Architecture (cont'd)

SPECIALIZED ‘SPATIAL’ S/W


Research Issues

Open fields of interest

• fuzzy information • graphical query languages • query optimization• spatio-temporal issues • system synergy...


26


Research Issues:Fuzzy Information

• Several kinds of fuzziness

• Fuzzy operators• Imprecise object boundaries

• … and more


Research Issues:Fuzzy Information (cont'd)

• Fuzzy operators

from …

to ...

very close close far very far1

0

true

false

very close close far very far

distance

distance


27


Research Issues:Graphical Query Languages

• Pictorial Query-By-Example (PQBE) [PS95]

A

C

BD

F

GE

J

HI

symbolic image

Query: “Find all objects northeast of object E”

EP_X

skeleton image

G J

results


Research Issues:Query Optimization

Cost models for selection / join queries on different data distributions

• Proposals:• Fractal dimension of a data set [FK94]• Density surface of a data set [TS96]


28


Research Issues:Query Optimization (cont'd)

• Fractal dimensionthe fractal dimension d of a 2-dimensional data set varies between d=2

and d=3, with respect to the objects irregularity

• Density Surface


Research Issues:Spatiotemporal Data

• Examples Questions:

“When did ship A get close to the coast?”

or

“Did a collision between A and B happen, if yes when?”

AB

Ship navigation


29


Research Issues:Spatiotemporal Data (cont'd)

• Examples (cont'd)Fire monitoring

Questions:

“Which is the shortest distance between the fire front and the town?”

or

“What are the speed and direction of the fire front at this moment?”

R

T

F3F2

F1


DSS

SDBMS

GIS

net

Research Issues:System Synergy

• The proposed model


30


FIREINFORMATION

METEOROLOGICALDATA

OTHERDATA

GEOGRAPHICAL DATA(digital form)

SATELLITE/AIRBORNEIMAGES, PAPER MAPS

AIOLOS-F(forest fire simulator)

FIREGEOGRAPHIC

DATABASE

DATAPROCESSING

INPUTINTERFACE

DISPLAYMONITORING

AIOLOS-FINTERFACE

GDS-GIS

FIRE-FRONTTEMPERATURES

WINDPARAMETERS

OTHEROUTPUTS

REAL-TIME DATA

DATA IN BATCH MODE

MEFISTO SYSTEM

Research Issues:System Synergy (cont'd)

An exampleMEFISTOTM


Summary:Need more work

• Extend standard DBMS architectures with• representations for spatial data types spatial operators • spatial indexes• access methods for spatial indexes • optimizer extensions • query language extensions to cover spatial queries • user interface extensions to handle graphical interaction, input-

output of spatial data and relationships, etc.


31


Summary:What is coming next?

• Some of the issues we find intriguing

Benchmarking

• Define statistically well founded workloads for a variety of applications

• Provide an environment which includes an attractive user interface and tools for visualisation



Performance Evaluation of Access Methods

• Thorough experimental examination of the approaches to test the behavior under real workloads

• Evaluation with realistic query types

• Extensibility on the range of queries

• Scalability behavior with growing volumes of data


32



Query Optimization

• Relatively undeveloped in the area of spatial DBs

• In many cases, e.g. geographic DBs, the execution strategy chosen is not near-optimal; just barely reasonable execution order

• Systematic cost estimates of different execution strategies are needed

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Spatial Databases and Spatial Indexing Techniques - … Databases and Spatial Indexing Techniques ... Spatial Databases and Spatial Indexing Techniques ... •Query Processing and