On Random Sampling over Joins

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On Random Sampling over Joins

• Surajit Chaudhuri Rajeeve Motwani Vivek
  Narasayya
• Microsoft Research Stanford University
  Microsoft Research
• Compiled by
• Arjun Dasgupta

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CONTENTS

• The difficulty of join sampling
• Semantic and algorithms of sample
• Two previous sampling strategies
• New strategies for join sampling
• Experiments results

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• SAMPLE (R1gtltR2,f)
• ?
• SAMPLE (R1,f) gtlt SAMPLE (R2,f)

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STRATEGY USED

• Obtain SAMPLE (R1gtltR2,f) from non-uniform samples
  of R1 and R2

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The Difficulty of Join Sampling -Example

• Suppose that we have the relations

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TECHNIQUES FOR SAMPLING

• Black Box U1 (un-weighted)
• Black Box U2 (un-weighted)
• Black Box WR1 (weighted)
• Black Box WR2 (weighted)

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Black-Box U2 Given relation R with n tuples,
generate an unweighted WR sample of size r.

• 1.
• 2. Initialize reservoir array A1..r with r
  dummy values.
• 3. While tuples are streaming by do begin
  (a) get
  next tuple t
  (b)
  (c) for
  j1 to r set Aj to t with probability 1/N end

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Black-Box WR2 Given relation R with n tuples,
generate a weighted WR sample of size r.

• 1.
• 2. Initialize reservoir array A1r with r dummy
  values.
• 3. While tuples are streaming by do begin
  (a) get next tuple t with weight w(t)
  (b)
  
  (c) for j1 to r do set Aj to t with prob.
  w(t)/W end.

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The Classification of the Problem

• Case A No information is available for
  either or .
• Case B No information is available for
  but indexes and /or statistics are available for
  .
• Case C Indexes/statistics are available for
  and .

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Previous Sampling Strategies

• Strategy Naive-Sample
• 1. Compute the join .
• 2. As the tuples of J stream by, use Black-Box
  U1
• or U2 to produce
  .

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Previous Sampling Strategies

• Strategy Olken-Sample
• 1. Let M be an upper bound on for all
  .
• 2.repeat
• (a) Sample a tuple uniformly at
  random.
• (b) Sample a random tuple from
  among all
• tuples that have
  .
• (c) Output with probability
  , and
• with remaining probability reject the
  sample.
• Until r tuples have been produced.

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New Strategies for Join Sampling

• Strategy Stream Sample
• 1. Use Black-Box WR1 or WR2 to produce a WR
  sample of size r, where the weight for
  a tuple is set to
  
• 2. While tuples of are streaming by do begin
  
• (a) get next tuple and let
  
• (b) sample a random tuple from
  among all
• tuples that have
• (c) output .
  end.

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New Strategies for Join Sampling

• Strategy Stream Sample is more efficiency then
  Olken
  1. No information is required for -
  case B.
  2. No tuple is
  rejected after computing the join .
  3.
  Only one iteration is needed for each output
  tuple.

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New Strategies for Join Sampling

• Strategy Group Sample
• 1. Use Black-Box WR1 or WR2 to produce a WR
  sample of size r, where the weight
  for a tuple is set to
  .
• 2. Let consist of the tuples
  . Produce
  whose tuples are grouped by s tuples
  that generated them.
• 3. Use r invocations of Black-Box U1 or U2 to
  sample r sample, one of each group.

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New Strategy for Join Sampling

• Strategy Frequency-Partition-Sample

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Experimental Results
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Experimental Results
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Experimental Results
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Summery

• The difficulty of join sampling- example.
• The classification of the problem - 3 cases.
• Naive-sample
  Olken-sample previous
  strategies
• Stream-sample
  Group-sample
  new strategies Frequency-partition-s
  ample
• Conclusion The new strategies are better then
  the earlier techniques.