A RuleBased Optimizer for Spatial Join Operations

1
A Rule-Based Optimizer for Spatial Join Operations

• Miguel Fornari
• João Luiz Comba
• Cirano Iochpe
• Instituto de Informática
• Universidade Federal do Rio Grande do Sul
• Porto Alegre - Brazil

2
Outline

• Introduction and motivation
• Spatial Hash Algorithms
• The Validation System Architecture
• The Rules
• Conclusions

3
Introduction and Motivation

• The spatial join operation is fundamental and
  expensive in GIS
• Combines two sets of spatial features based on a
  spatial predicate
• DBMS, traditionally, improves the performance
  based on heuristic rules and cost expressions
• Spatial DBMS can include a specific module to
  spatial operations

4
Goal

• Reduce response time of the spatial join
  algorithms for the filter step
• A set of rules to optimize the performance of
  some well-known algorithms
• Which parameters are relevant?
• What is the best value for each important
  parameter?

5
SJ Algorithms

• According to the file organization

6
SJ algorithms

• For each algorithm, two cost expressions are
  important
• I/O cost
• CPU cost
• Some cost are already known, but not all
• All expressions written in a similar notation

7
The System Architecture

• The performance analysis, although correct,
  simplifies many cases
• Real cases are more complex
• Real data sets obtained in Internet

8
Plane-sweep algorithm

• All SJ algorithms load objects to memory and
  perform a sweep-plane algorithm to check if pairs
  of objects satisfy the spatial predicate.
• Traditional performance is O(k n log n) , where
  k is the number of object intersections
• But, O(c n log n), where c is the number of
  performed comparisons, is more exact.

9
Plane-sweep algorithm

• Divide the space into strips
• Count the number of objects in each strip
• The size of strips is the average size of objects
  
• Estimation of c Sum of all values

10
Rule 1 Sweep-plane

• The DBMS can estimate c for each axle and choose
  the one with minor value of c, optimizing the
  plane-sweep.
• The shape of objects alters the response time

11
Synchronized Tree Transversal

• Well known algorithm for R-Trees
• The performance depends on height of R-Trees and
  average size of nodes.
• The space division reduces the number of object
  comparisons ( c).
• Available memory is not important.

12
Rule 2 - STT

• The STT algorithm is optimized defining nodes
  with a low number of entries.
• But, the total number of nodes will be greater,
  defining a minimum limit for the rule.
• Optimal value between 50-75

13
Rule 2 - STT

• The performance of STT algorithm is constant when
  the memory buffer size increases.
• Except for very values
• Set any value greater than 4heigth of the R-Trees

14
Iterative Stripped SJ

• Iterative SJ (Jacox Samet) strips
• Strips divides the space and reduces c
• Transpassant objects can occur
• The sorting can be either internal or external
• The performance depends on the memory available,
  the number of strips, and replicas.

15
Rule 3 - ISSJ

• The ISSJ algorithm is optimized definining a
  great number of strips. The number of objects in
  each strip will be small, but the is limited by
  the adding of replicas.

16
Rule 3 - ISSJ

• Its important allocate enough memory to perform
  an internal sorting of each set

17
Partition Based Spatial Method(PBSM)

• Calculates the number of partitions
• Uses a regular grid to divide the space
• Partitions can overflow
• The performance depends on the number of replicas
  and overflowed partitions
• The number of object comparisons (c) is reduced
  by the space subdivision

18
Rule 4 - PBSM

• PBSM is improved setting a high value for the
  number of partitions using a small size of memory
  or just set a lower bound to the number of
  partitions.

19
Rule 4 - PBSM

• This rule is limited by the number of replicas,
  that increase the number of processed objects.

20
Histogram Hash Stripped Join

• A histogram of object distribution guides the
  space partitioning to avoid overflow
• Replicas are counted into the histogram
• The objects are maintained in a hash file and are
  loaded to memory only once.
• The performance is affected by the number of
  replicas and the space subdivision

21
Rule 5 - HHSJ

• HHSJ is improved setting a large value for the
  number of partitions and for the number of strips.

22
Rule 5 - HHSJ

• This rule is limited, also, by the number of
  replicas, that increase the number of processed
  objects.

23
Conclusions Future Work

• Our main contribution
• The use of rules can reduce the response time of
  individual algorithms, in some cases, more than
  50.
• The rules can be incorporated in real GDBMS
• Future work
• Use 3D sets to perform the tests
• Include other spatial operations
• Implement in PostGIS

24
Contact questions

• Miguel Fornari
• fornari_at_ieee.org
• www.inf.ufrgs.br/fornari
• João Comba
• comba_at_inf.ufrgs.br
• www.inf.ufrgs.br/comba
• Cirano Iochpe
• ciochpe_at_inf.ufrgs.br
• www.inf.ufrgs.br/ciochpe