A Paper on RANDOM SAMPLING OVER JOINS by SURAJIT CHAUDHARI RAJEEV MOTWANI VIVEK NARASAYYA

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A Paper on RANDOM SAMPLING OVER
JOINSbySURAJIT CHAUDHARIRAJEEV MOTWANIVIVEK
NARASAYYA

• PRESENTED BY,
• JEEVAN KUMAR GOGINENI
• SARANYA GOTTIPATI

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Outlines

• Introduction
• Semantics of Sample
• Algorithms of Sampling
• Join Sampling Problem
• New Strategies for Join Sampling
• Extensions and Negative Results
• Experimental Evaluations
• Conclusions

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Terms Used

• SAMPLE(R, f) is an SQL operation.
• f is a fraction of a relation R.
• Relation R is produced when a query Q is
  evaluated.

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Introduction

• Sampling the output of query is inefficient.
• OLAP and Data Mining use sample of the result of
  the query posed.
• Sampling must be supported on the result of an
  arbitrary SQL query.

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Continued

• Supports Random Sampling as a primitive
  relational operation in relational databases.
• SAMPLE(R, f) operation.
• Partially evaluate Q to generate a sample of R.
• Sample operation appears arbitrarily in query
  tree T.
• Commute the sample operation down the tree using
  a single join operation.

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Semantics of Sample

• 1. Sampling with Replacement (WR)
• 2. Sampling without Replacement (WoR)
• 3. Independent Coin Flips (CF)
• Sample with probability f independent of other
  tuples.
• f- Fraction of Tuples in R
• n- Number of Tuples in R

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Algorithms for Unweighted Sequential WR Sampling
Black-Box U1 Given relation R with n tuples, generate an UNWEIGHTED WR sample of size r. Black-Box U2 Given relation R with n tuples, generate an UNWEIGHTED WR sample of size r.

• The size of relation being sampled.
• How it scans the relation?
• Need any significant auxiliary memory?

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Algorithms for Weighted Sequential WR Sampling
Black-Box U1 Given relation R with n tuples, generate an WEIGHTED WR sample of size r. Black-Box U2 Given relation R with n tuples, generate an WEIGHTED WR sample of size r.

• The size of relation being sampled.
• How it scans the relation?
• Need any significant auxiliary memory?

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The Difficulty of Join Sampling
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Classification of the Problem

• Case A No information is available for either
  R1 or R2
• Case B No information is available for R1
  but indexes and /or statistics are available
  for R2.
• Case C Indexes/statistics are available for
  R1 and R2

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Previous Sampling Strategies

• Strategy Naive-Sample
• Strategy Olken-Sample

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New Strategies for Join Sampling

• Three new strategies of Sampling are
• Strategy Stream Sample.
• Strategy Group Sample.
• Strategy Frequency-Partition-Sample.

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Table showing the information about R1 and R2
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Strategy Stream Sample

• Performs only a sequential sample from R1
• Does not generate excess tuples

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Strategy Group Sample
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Strategy Frequency-Partition-Sample

• Assumption that we have full statistics for R2
• Uses strategy Group Sample for high frequency
  values.
• Strategy Naive Sample for low frequency values.
• Join attribute values need not be of high
  frequency in both operand relations.
• Determine the distribution of the sample between
  high and low frequency sub domain.
• Advantage It needs summary statistics in the
  form of histograms for R2.

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Continued
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Extensions and Negative Results

• The Inherent difficulty of Join Sampling
• Even if we have large samples from R1 and R2
  and the detailed statistics, it is not possible
  to generate any non-empty random sample of R1
  join R2.
• Dealing with Join Trees
• Pushing down the Sample operation to the
  operands.

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Experimental Evaluations

• Naïve Sample Add U1 operator as the root of tree
• Olken Sample Create uniform random sample T from
  key values of R1
• Stream Sample Insert WR1 operator as a child of
  the join operator
• Frequency-Partition-Sample Implement a modified
  version of WR1 operator for producing random
  sample from R1

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Experimental results
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Continued
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Continued
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Conclusions

• Study of issues involved in implementing sampling
  as primitive operation.
• Series of Sampling Strategies
• Provided new schemes for sequential random
  sampling for uniform and weighted sampling
  distributions
• Even more efficient strategies can be developed

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• QUESTIONS??
• Thank you