SFTree and Its Application to OLAP

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SF-Tree andIts Application to OLAP

• Speaker Ho Wai Shing

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Overview

• Introduction
• Basic OLAP technologies ROLAP and MOLAP
• Structure of an SF-Tree
• Using SF-Tree for OLAP
• Conclusion

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Introduction

• On-line Analytical Processing (OLAP) is an
  important tool for decision making
• Users may ask for the aggregated measure
  attributes for different combination of dimension
  attributes GrayBLP96.

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Introduction -- OLAP

• e.g., in the CarSales table of a data warehouse
• CarSales(TransID, Buyer, Date, Shop, Color,
  Price)
• The users may want to know the total sales of the
  yellow cars sold in Sept, 2002.

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Introduction -- OLAP
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Introduction -- OLAP

• i.e., answer 60k
• To answer this efficiently, usually the answers
  are precomputed and stored
• A popular data model is called data cube
  GrayBLP96.

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Introduction -- OLAP
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Introduction -- OLAP

• Note that we're referring to the model only, not
  every entry is materialized
• every combination of dimensions are included
  (so, here, it's just one example cuboid, other
  cuboids include , , etc)

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Introduction -- OLAP

• Research issues To store this information with
  high space efficiency and/or high query speed.

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ROLAP and MOLAP
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ROLAP and MOLAP

• In a data cube, we have to store the combinations
  of dimension values and the associated aggregate
  values.
• ROLAP (Relational OLAP) stores the entries of the
  mapping in relational tables.
• MOLAP (Multi-dimensional OLAP) stores the entries
  in a multi-dimensional array.

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ROLAP and MOLAP

• A materialized MOLAP multidimensional array (for
  colour and shop)

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ROLAP and MOLAP

• A ROLAP table that stores the entries (for colour
  and shop)

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ROLAP and MOLAP

• MOLAP adv
• quick 1 retrieval for 1 point query (i.e., use
  the dimension values to calculate the address of
  the aggregated value stored)
• may be space efficient if the cube is very dense
  (since all dimensions are not explicitly stored
  in every tuple)

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ROLAP and MOLAP

• MOLAP disadv
• space inefficient if the cube is sparse (has many
  zero entries) esp. for high dimensional cases.
• eased by chunking
• may need a lot of scans if we issue a large range
  query (i.e., involves many dimension values)

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ROLAP and MOLAP

• ROLAP
• index are built on the table to improve query
  performance
• e.g., B-Tree on each dimension, or R-Tree over
  all points.
• ROLAP Adv
• space efficient (non-zero entries are not stored)

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ROLAP and MOLAP

• ROLAP Disadv
• indexes, such as R-Tree, may not be effective in
  high-D data
• Many joins are required to produce the result (if
  single D indexes are used)
• Intermediate result may be large
• Can we do better?

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SF-Tree
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SF-Tree

• stands for Signature File Tree
• stores a mapping from objects to integer
  flexibly, efficient and has a statistical
  accuracy guarantee

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SF-Tree

• Basic Idea
• divide the objects into groups of the same (or
  similar) associated number.
• checking the associated number of an object is
  the same as checking which group this object
  belongs.
• signature files are used to improve the
  efficiency of existence checking, trees are used
  to improve accuracy and speed.

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SF-Tree
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SF-Tree

• Properties (Adv)
• Space efficient, independent of object size
• Flexible, can have a tradeoff among space, speed
  and accuracy
• Speed is independent of number of objects

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Using SF-Tree for OLAP
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Using SF-Tree for OLAP

• The information in OLAP can be modeled as a
  mapping from objects (dimension values) to
  numbers (aggregate values).
• Thus we can use SF-Tree to store this mapping.

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Using SF-Tree for OLAP

• e.g., (TST, Yellow) is an object, it's associated
  number is 10k
• we can insert it into SF-Tree
• space requirement
• m/ln2 bits per object per level
• independent of object size (i.e., dimensionality)
• smaller than ROLAP esp. for high-D

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Using SF-Tree for OLAP

• Adv
• more space efficient than ROLAP (definitely much
  better than MOLAP)
• quicker than ROLAP in point queries (no need to
  do joins)
• Disadv
• range queries require scanning all possible
  points in query range (as in MOLAP).

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Using SF-Tree for OLAP

• To avoid the disadvantage, we borrow the idea
  from MRA-Tree LazM01
• MRA-Tree (Multi-Resolution Aggregate Tree)
• in a data/space partitioning tree, add aggregates
  in all internal nodes.
• one example is quad-tree aggregates.

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MRA-Tree
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MRA-Tree
580k
160k
60k
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MRA-Tree

• For answering range queries, the number of
  accesses is reduced
• Extra space is required
• Leaf nodes may not contain only 1 record
• The tree size drop significantly if we increase
  the number of points in a leaf node page.

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MRA-Tree
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MRA-Tree
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SF-Tree with MRA-Tree

• SF-Tree is more space efficient than ROLAP
• Use SF-Tree to store leaf nodes
• each page thus can store more points
• tree size/depth is reduced
• less page accesses in query

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SF-Tree with MRA-Tree

• Adv
• more space efficient, i.e., may be small enough
  to fit in memory and reduce page accesses, esp.
  for high-D data
• Disadv
• still need to scan the area in leaf nodes (vs.
  scanning data points while using ROLAP)

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Conclusion

• SF-Tree is space efficient, can be used to store
  a data cube. (or may be used as a ROLAP index)
• Though in analysis the speed of SF-Tree is poor
  for range queries, we try to incorporate the idea
  in MRA-Tree on SF-Tree to increase the speed.

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Reference

• GrayBLP96 J. Gray, A. Bosworth, A. Layman, and
  H. Piramish. Data cube A relational aggregation
  operator generalizing group-by, cross-tab, and
  sub-total. In ICDE'96.
• LazM01 I. Lazaridis, and S. Mehrotra.
  Progressive Approximate Aggregate Queryies with a
  Multi-Resolution Tree Structure. In SIGMOD'01.