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Efficient search indices for geospatial data in a relational database. Gyorgy (George) Fekete Dept. Physics and Astronomy Johns Hopkins University. Acknowledgements. Alex Szalay NVO, SDSS, iVDGL, ... Jim Gray Databases, SQL Server Ani Thakar, Tamas Budavari - PowerPoint PPT Presentation
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G. Fekete, JHU
Efficient search indices for geospatial data in a relational database
Gyorgy (George) FeketeDept. Physics and Astronomy
Johns Hopkins University
G. Fekete, JHU
Acknowledgements
• Alex Szalay– NVO, SDSS, iVDGL, ...
• Jim Gray– Databases, SQL Server
• Ani Thakar, Tamas Budavari– SDSS pipeline, Geometric libraries
G. Fekete, JHU
Motivation
• Growth of volume of data– terabytes per day
• Increasing importance of databases in managing science data
• Data mining : potential for new discoveries• Cross matching between multiple surveys• Much of this data is distributed on a sphere
– astronomy and earth science– great interest in a universal, computer-friendly index
on the sphere
G. Fekete, JHU
Astronomy Data
• “old days” – astronomers took photos.
• Since the 1960’s– they began to digitize.
New instruments are digital (100s of GB/nite)Detectors are following Moore’s law.Data avalanche: double every 2 years
G. Fekete, JHU
Astronomy Data
• Astronomers have a few Petabytes now.
• Data volume and ownership– doubles every 2 years.– Data is public after 2 years.– So, 50% of the data is public.– Some have private access to 5% more data.
• But…..– How do I get at that 50% of the data?
G. Fekete, JHU
New Astronomy
• Data “Avalanche”– the flood of Terabytes of data– present techniques of handling these data do not
scale well with data volume
• Systematic data exploration– will have a central role– statistical analysis of the “typical” objects– automated search for the “rare” events
• Digital archives of the sky– will be the main access to data
G. Fekete, JHU
Data Intensive Science
• Data avalanche in astronomy and other sciences– old file-based solutions do not cut it– old data silos don’t work– old programming models don’t work
• We have some new tricks!• Astronomy and Earth-Science
– methods presented here deal with the topology and the geometry of the sphere
G. Fekete, JHU
One Of These Tricks:
• Map regions of the sphere to unique identifiers that can be used as references to those areas– elementary spherical geometry to identify a
region– multi-resolution– compactly describe areas at arbitrary
granularity
G. Fekete, JHU
Support Spatial Searches
Typical queries– What is near this point?– What objects are in this area?– What areas overlap this area?
G. Fekete, JHU
Design Considerations
• Has to – work with a relational database– represent areas of interest precisely– be scalable– be coordinate system neutral– maintain consistency with the topology of the sphere
• Approach:– precise mathematical description of regions– methods for covering a region with an optimal set of
discrete descriptors (trixels)– covermap of trixels used for accelarated query
G. Fekete, JHU
Components
• Region descriptions (continuous part)– region, convex, halfspace– API and a text language to describe– XML for inter-service, inter-application object transfer
• Hierachical Triangular Mesh (discrete part)– trixels– covermaps
• Database– extend the DB server engine with spatial access
methods– implementing coarse filtering with table valued
functions
G. Fekete, JHU
Continuous Part: A Region
Region– is the union of convexes
Convex– is intersection of halfspaces
Halfspace– simple search cone– circle
G. Fekete, JHU
Examples of Convexes
• Disk, Circle, Search cone, ...
• Spherical Polygon– yes, it is actually a convex (adj.) convex (n.)
• Band
• Lat/Lon (or Ra/Dec) rectangle
• anything else...
G. Fekete, JHU
Halfspace
Cutting plane makes two halfspaces
Oriented plane makes one well defined halfspace
G. Fekete, JHU
Halfspace
Completely defined by (directed) plane normal and distance along the normal
D = cos (cone halfangle)
h = (x, y, z, D)
G. Fekete, JHU
Point Inclusion In Region(x,y,z)
P
Q
P . (x, y, z) > D
h = (x, y, z, D)
Q . (x, y, z) < D
Point is inside a convex if and ony ifit is inside all halfspaces
Point is inside a region if and ony ifit is inside at least one convex
G. Fekete, JHU
Disconnected Components
• Intersecting halfspaces can produce multiple connected components
• Anything you can think of can be expressed as a union of convexes
G. Fekete, JHU
Triangle Subdivision Scheme
Each trixel can be named:eg S123222102
HTMId: depth limited trixels are represented 64-bit integers
G. Fekete, JHU
HTMId Coherence
1023 4092 - 4095 16368 - 16383
level 3 level 4 level 5
17575006175232 - 17592186044415level 20
G. Fekete, JHU
Covermap Of Circle
covermap
is a set of trixels that cover a region
G. Fekete, JHU
Covermap Of California
15277198671872 - 1527827241369515298673508352 - 1530082099199915301089427456 - 15302968475647... ...15384572854272 - 15384841289727 44 trixels, but only 13 ranges
Use covermaps and HtmIDs to coarse filter...
G. Fekete, JHU
Database Part
1. From table of objects, consider only those whose key values are in the covermap
2. Of those that passed, perform calculation to complete query
3. Return result in table
G. Fekete, JHU
Coarse and Fine Filtering In Queries
Coarse Subset
All Objects
Reje
ct
AcceptFineFilter
Coarse FilterCoarse Subset
All Objects
Reje
ctR
eject
AcceptAcceptFineFilterFineFilter
Coarse FilterCoarse Filter
use covermaps
use precise calculations
G. Fekete, JHU
Usage of Tables and Index Keys
Create a function that generates keys that cluster related data together
– if objects A and B are nearby, then the keys for A and B should be also be nearby in the Index space
– HtmID
Create a table-valued function that returns– list of key ranges (the covermap) containing all the
pertinent values– covermap
G. Fekete, JHU
Caveats
• You cannot always get every key to be near all its neighbors– keys are sorted in one dimension– relatives are near in two-dimensional space
• But we can come close– The ratio of false-positives to correct answers
is a measure of how well you are doing.
.
G. Fekete, JHU
Sample Covermap
select * from fHtmCoverCircleLatLon(39.3, -76.6, 100)
HtmIDStart HtmIDEnd---------------- ----------------14023336656896 1402414196326314024410398720 1402521570508714025484140544 14027363188735
G. Fekete, JHU
Places Within 100 Miles Of Baltimore
select ObjIDfrom SpatialIndex join fHtmCoverCircleLatLon(39.3, -76.6, 100) On HtmID between HtmIDStart and HtmIDEndwhere Type = 'P' and dbo.fDistanceLatLon(39.3, -76.6, Lat, Lon) < 100go
Number of rows in cover join (coarse filter) 2223Number of rows that are within 100 n. miles (after the fine filter). 1122 Number of places in DB 22993Time with covermap 35Time without covermap 100
G. Fekete, JHU
California As A Regiondeclare @californiaRegion varchar(max)set @californiaRegion = 'REGION ' + 'rect latlon 39 -125' -- nortwest corner + '42 -120 ' -- center of Lake Tahoe + 'chull latlon 39 -124 ' -- Pt. Arena + '39 -120 ' -- Lake tahoe. + '35 -114.6 ' -- start Colorado River + '34.3 -114.1 ' -- Lake Havasu + '32.74 -114.5 ' -- Yuma + '32.53 -117.1 ' -- San Diego + '33.2 -119.5 ' -- San Nicholas Is + '34 -120.5 ' -- San Miguel Is. + '34.57 -120.65 ' -- Pt. Arguelo + '36.3 -121.9 ' -- Pt. Sur + '36.6 -122.0 ' -- Monterey + '38 -123.03 ' -- Pt. Rayes
G. Fekete, JHU
California Cities
select PlaceName from Place where HtmID in (select distinct SI.objID from fHtmCoverRegion(@californiaRegion) loop join SpatialIndex SI on SI.HtmID between HtmIdStart and HtmIdEnd and SI.type = 'P' join place P on SI.objID = P.HtmID cross join fHtmRegionToTable(@californiaRegion) Poly group by SI.objID, Poly.convexID having
min(SI.x*Poly.x + SI.y*Poly.y + SI.z*Poly.z - Poly.d) >= 0)
OPTION( FORCE ORDER)
This is a popular query, so we can include it as a stored procedure
See Point Inclusion
G. Fekete, JHU
Point Inclusion With SQL(x,y,z)
P
P . (x, y, z) > D
h = (x, y, z, D)
P . (x, y, z) - D > 0
min(SI.x*Poly.x + SI.y*Poly.y + SI.z*Poly.z - Poly.d) >= 0)
G. Fekete, JHU
Covermap Of California
15277198671872 - 1527827241369515298673508352 - 1530082099199915301089427456 - 15302968475647... ...15384572854272 - 15384841289727 44 trixels, but only 13 ranges
Use covermaps and HtmIDs to coarse filter...
G. Fekete, JHU
DB Function For Region Search
select PlaceName from Placewhere HtmID in(select ObjID
from fHtmRegionObjects(@californiaRegion,'P'))
Number of rows in cover join (coarse filter) 981Number of rows that are within region 885 Number of places in DB 22993Time with covermap 110Time without covermap 1210
G. Fekete, JHU
SDSS
• Digital map in 5 spectral bands covering ¼ of the sky.
• Will obtain 40 TB of raw pixel data.• Photometric catalog with more than 200 million
objects.• Spectra of ~ 1 million objects.• Data Release 3 – DR3: 150 M images, 480 k
spectra.
G. Fekete, JHU
Ambitious Survey
• Info content > US Library of Congress
• Before SDSS:total number of galaxies with measured parameters ~ 100k
•After SDSS, we will have detailed parameters forover 100 Million galaxies!!
G. Fekete, JHU
SDSS Processing Pipeline
• Processed data ingested into a relational DBMS• Allows fast exploration and analysis - Data Mining• Heavily indexed to speed up access – HTM + DB Indices• Short queries can run interactively.• Long queries (> 1 hr) require a custom Batch Query
System.
G. Fekete, JHU
SDSS Data Access
• Data Archive Server (DAS)– FITS files (raw data)– Images, spectra, corrected frames, atlas images,
binned images, masks– Online form-based access at www.sdss.org– Rsync and wget file retrieval
• Catalog Archive Server (CAS)– Science parameters extracted to catalogs– Stuffed into relational DBMS (SQL Server)– Online access via SkyServer at http://cas.sdss.org/,
http://skyserver.sdss.org
G. Fekete, JHU
Conclusion
• HTM methods provide means for implementing ways to filter data so that expensive geometrical computations to satisfy a query are performed on only a small subset of the original data
• The HTM is on its way to become one of the de facto standards for representing spatial information in astronomical catalogs, especially for large-scale surveys.
