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https://issues.apache.org/jira/browse/CALCITE-4132?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Liya Fan updated CALCITE-4132:
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    Description: 
Currently, we estimate the NDV of many operators based on the 
RelMdUtil#numDistinctVals method. This method estimates the expected number of 
distinct values selected n times (with replacement) from a collection with N 
distinct values. The estimation is based on the approximation when N approaches 
infinity.

However, when N is not a large number, the difference between the approximate 
and exact values can be notabe. In addtion, the error can be magnified by 
different combinations of N and n, which can lead the optimizer to make wrong 
decisions. 

For example, when we select one element from a table with a 4-value enum, we 
expect to get one distinct value according to common sense. However, the 
current implementation gives 0.88, which is counter-intuitive, and leads to a 
10+% error. 

Therefore, we give the exact estimation based on the unbiased estimator (The 
proof is given in the comment). 

  was:
Currently, we estimate the NDV of many operators based on the 
RelMdUtil#numDistinctVals method. This method estimates the expected number of 
distinct values selected n times (with replacement) from a collection with N 
distinct values. The estimation is based on the approximation when N approaches 
infinity.

However, when N is not a large number, the difference between the approximate 
and exact values can be notabe. In addtion, the error can be magnified by 
different combinations of N and n, which can lead the optimizer to make wrong 
decisions. 

Therefore, we give the exact estimation based on the unbiased estimator (The 
proof is given in the comment). 


> Estimate the number of distinct values more accurately
> ------------------------------------------------------
>
>                 Key: CALCITE-4132
>                 URL: https://issues.apache.org/jira/browse/CALCITE-4132
>             Project: Calcite
>          Issue Type: Improvement
>          Components: core
>            Reporter: Liya Fan
>            Assignee: Liya Fan
>            Priority: Major
>              Labels: pull-request-available
>          Time Spent: 20m
>  Remaining Estimate: 0h
>
> Currently, we estimate the NDV of many operators based on the 
> RelMdUtil#numDistinctVals method. This method estimates the expected number 
> of distinct values selected n times (with replacement) from a collection with 
> N distinct values. The estimation is based on the approximation when N 
> approaches infinity.
> However, when N is not a large number, the difference between the approximate 
> and exact values can be notabe. In addtion, the error can be magnified by 
> different combinations of N and n, which can lead the optimizer to make wrong 
> decisions. 
> For example, when we select one element from a table with a 4-value enum, we 
> expect to get one distinct value according to common sense. However, the 
> current implementation gives 0.88, which is counter-intuitive, and leads to a 
> 10+% error. 
> Therefore, we give the exact estimation based on the unbiased estimator (The 
> proof is given in the comment). 



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