1. Native Multidimensional Indexing in Relational Databases
David Hoksza, Tomáš Skopal
Charles University in Prague Department of Software Engineering Czech Republic

2. Presentation Outline Multidimensional querying Indexing in PostgreSQL
attribute number growth
indexing methods
contemporary DB systems
Indexing in PostgreSQL
user-defined access methods
external indexing
framework
Experiments
COMAD 2008

3. Indexing Single-attribute based indexing
to avoid sequential scan
B-tree
Multi-attribute based indexing
window query
straightforward solution – multiple B-trees
SELECT * FROM Products
WHERE
BrandID BETWEEN (3 AND 11)
SELECT * FROM Products
WHERE
BrandId BETWEEN (13 AND 14)
AND
ProductTypeID BETWEEN (13 AND 24)
PeriodID BETWEEN (3 AND 11)
COMAD 2008

4. Multi-attribute Based Indexing
Multiple B-trees
attribute number growth
→ exponential growth of partial result-sets
→ sequential scan
dimensionality curse
COMAD 2008

5. Multi-dimensional access methods
B+-tree with Compound Keys
most often employed solution
multiple keys – single chained value
key components compared in lexicograhpical order
assymetry in the order of the keys
R-tree
UB-tree
transformation of n-dim points into 1-dim Z-address → Z-curve
Z-curves divided into Z-regions indexed by a B+-tree
COMAD 2008

6. Native Multi-dimensional Indexing
SELECT * FROM Products
WHERE
BrandId BETWEEN (13 AND 14)
AND
ProductTypeID BETWEEN (13 AND 24)
PeriodID BETWEEN (3 AND 11)
Table rows
points in n-dimensional space
R-tree
Queries
cubes in n-dimensional space (n-dimensional windows)
COMAD 2008

7. Contemporary DB systems
COMAD 2008

8. PostgreSQL Object-relational DBMS Open-source
Since 2005 (v. 8.0) runs on Windows
Emphasis on extensibility
data types
operators
procedural languages
access methods …
COMAD 2008

9. Relation Types in PostgreSQL
Heap relations (HRs)
user relations
system catalog
undefined order
Index relations (IRs)
<key,value> pairs
external
fast access to heap relations
internal
access methods’ structures
COMAD 2008

10. User-defined Access Methods (AM) in PostgreSQL
Implement a set of functions communicating with PostgreSQL’s core (AM implementation).
Register the functions (located in libraries).
Define an AM (index type) by connecting the functions with a newly created AM.
Establish a class of operators and types for the AM.
Use the index.
COMAD 2008

11. User-defined Access Methods in PostgreSQL – cont.
required functions
index_build
creating a structure
index_insert
inserts a record
index_beginscan
starts a new scan
index_gettuple
gets a record fulfilling search conditions
index_getmulti
gets a set of records
index_endscan
finishes a search
index_markpos
marks actual position in a scan
index_restrpos
returns to a marked position
index_rescan
repeats scan with the same structure of search keys
index_bulkdelete
removes a set of records
index_costestimate
estimates cost of a search
COMAD 2008

12. External Indexing
AM in PostgreSQL store data in IRs returning IRs’ TIDs to the core
External indexing framework
Storing IRs’ TIDs in external index storage
PostgreSQL’s interface to access methods still requires high level of mastering of PostgreSQL’s inner mechanisms
Framework for external indexing
COMAD 2008

13. Framework interface void FW_CreateStructure (Relation index_relation);
void* FW_PrepareInsert (Relation index_relation);
void FW_InsertTuple (void *fw_data, Relation index_relation, IndexTuple index_tuple, BlockNumber block_number, OffsetNumber offset);
void FW_FinishInsert (void *fw_data);
void FW_InitSearch (IndexScanDesc scan, ScanDirection dir);
bool FW_GetNextTID (IndexScanDesc scan, ScanDirection dir, BlockNumber *block_number, OffsetNumber *offset);
void FW_DeleteTuple (BlockNumber block number, OffsetNumber offset);
COMAD 2008

14. Experimental evaluation
The testbed
Uniform
clusters of uniformly distributed (up to 15-dimensional) objects
Gauss
(up to 3-dimensional) objects following Gaussian distribution
DBLP
435,373 DBLP database records
author, type of publication, year of publication, number of pages
Studied costs
index access count
real-time
COMAD 2008

15. Experiments – Database Growth
COMAD 2008

16. Experiments – Query Selectivity
COMAD 2008

17. Experiments – Dimension Growth
COMAD 2008

18. Experiments – Real-time
COMAD 2008

19. Conclusion We have proposed and implemented Results show
Native multidimensional indexing by R-tree
Indexing framework for PostgreSQL
Implementation of native external R-tree index
Results show
big speed-up on the real-world data according to index-access metric
poor physical implementation of access methods in PostgreSQL in comparison to Oracle and MSSQL Server
COMAD 2008