Range CUBE: Efficient Cube Computation by Exploiting Data Correlation

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Range CUBE Efficient Cube Computation by
Exploiting Data Correlation

• By
• Rushabh Ajmera

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Outline

• Problems Faced by Data Cube
• Range Cubing to the Rescue
• How Range Cube achieves it
• Example of Range cube
• Range Cube Algorithm
• Range cube Experimental Results

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Problems faced by Data cube

• Prohibitively Expensive
• Loss of format semantics
• Loss of precision
• efficient data structure supporting this
  definition
• High disk i/o time

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Solution

• H-Cubing
• Star Cubing
• Condensed Cube
• Quotient Cube
• Range cube

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Range Cubing Features

• Efficient ways to compute data cube
• Efficient way to compress data cube
• No loss of precision
• Preserve the roll-up/drill-down semantics
• Efficient w.r.to H-cubing (1/13th)
• Less than one ninth of the space of full cube

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Range cube Features (cont..)

• Semantic preserving and format preserving of
  native data cube
• Work easily with wide range of current database
  and data mining apps
• Less sensitive to dimension order
• Other indexing or compression techniques such as
  dwarf can be applied
• Can incorporate performance approaches

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How does Range cube achieve this ?

• Using a new data structure called RANGE TRIE
  which is used to compress and identify
  correlation
• A range trie captures data correlation by finding
  dimension values that imply dimension values.

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Whats Trie

• Trie of size (h, b) is a tree of height h and
  branching factor b
• All keys can be regarded as integers in range 0,
  bh
• Each key K can be represented as h-digit number
  in base b K1K2K3Kh
• Keys are stored in the leaf level path from the
  root resembles decomposition of the keys to digits

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Efficiency of cube computation comesfrom the
three aspects

• It compresses the base table into a range trie,
  so that it will calculate cells with identical
  aggregation values only once.
• The traversal takes advantage of simultaneous
  aggregation, that is, the m - dimensional cell
  will be computed from a bunch of (m 1) -
  dimensional cells after the initial range trie is
  built. At the same time, it facilitates Apriori
  pruning.
• The reduced cube size requires less output I/O
  time.

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Base Table
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The lattice of cuboids derived from the base table
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Construction of Range Trie
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Construction of Range Trie
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Information stored in Range Trie

• Dimension Values of tuples determine the
  structure of a range trie, and are stored in the
  nodes along paths from the root to leaves.
• Measure Values determine the aggregation values
  of the nodes.

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Properties of a Range Trie

• The maximum depth of the range trie is the number
  of dimensions n.
• The number of leaf nodes in a range trie is the
  number of tuples with distinct dimension values,
  which is bounded by the total number of tuples.
• Because siblings have distinct values on their
  start dimension, the fan-out of a parent node is
  bounded by the cardinality of the start dimension
  of its child nodes.
• Each interior node has at least two child nodes,
  since its parent node contains all dimension
  values common to all child nodes.
• Each node represents a set of tuples represented
  by the leaf nodes below it.

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Range Trie Construction
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Size of Range Trie

• Suppose we have a range trie on a D-dimensional
  dataset with T tuples.
• The depth of the range trie is D in the worst
  case, when the dataset is very dense and the trie
  structure is like a full tree.
• It is logNT in the average case, for some N, the
  average fan-out of the nodes.

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Range cubing Vs. H- cubingEvaluating the
effectiveness
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Evaluating the impact of skewnessDimension6,card
iniality100, no. of tuples 200K
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Evaluating the impact of sparsitydimension6,
tuples200k ,cardiniality10.10000
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Evaluating performance on real Data set weather
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Future Work

• Incorporating constraints with range cube
  computation
• Dealing with holistic funcitons
• Applying different compression technique to
  compress cube
• Supporting incremental and batch updates

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Questions ?