Github user jkbradley commented on the pull request:

    https://github.com/apache/spark/pull/3702#issuecomment-67428833
  
    We're in agreement.  My earlier statement "The simplistic approach should 
never be off by more than numPartitions." meant that the total count would 
never be off by more than numPartitions, i.e., +/- 1 per partition.
    
    Are you asking about oversampling?  If so, then I had these 2 options in 
mind for approximations:
    
    1. In each partition, take samples evenly spaced ceil(rdd.count / 
numPartitions) apart.  Return however many bins you get back.  The # of bins 
will be approximate, and the bin spacing (i.e., the # of elements in each bin) 
will vary a little across bins.
    2. Do the same, but take extra samples (3X ?) and then take exactly numBins 
samples on the driver.  The # of bins returned will be exact, and the bin 
spacing will be a little more uniform.


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