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Performance Summary of Algorithms based on Hashing

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• Summary
  • Summary:

    Operator Symbol	Operation	Memory buffer requirement	# Disk I/O operations
    σC(R)	selection	N/A (use one-pass algorithm)	N/A
    πattrs(R)	projection	N/A (use one-pass algorithm)	N/A
    δ(R)	duplicate elimination	M   ≥   sqrt(   B(R)   ) + 1	3 B(R)
    γL(R)	grouping	M   ≥   sqrt(   B(R)   ) + 1     (hash using the grouping attrs)	3 B(R)
    R ∪ S	Union	M   ≥   sqrt(   min ( B(R), B(S) )   ) + 1	3 B(R) + 3 B(S)
    R ∩ S	Intersection	M   ≥   sqrt(   min ( B(R), B(S) )   ) + 1	3 B(R) + 3 B(S)
    R − S	Difference	M   ≥   sqrt(   min ( B(R), B(S) )   ) + 1	3 B(R) + 3 B(S)
    R × S	Product	does not help   (use nested-loop cartesian product algorithm)	N/A
    R ⋈ S	Join	M   ≥   sqrt(   min ( B(R), B(S) )   ) + 1	3 B(R) + 3 B(S)

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• Final comments
  • Important assumption in hash-based 2-pass algorithms:

    The hash-based 2-pass algorithms rely on the important assumption that: In phase 1, the input relation(s) R (and S) are uniformly hashed into their buckets so that: 1 B(Ri) = --- B(R) for each fragment Ri M-1

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  • What to do when input relation(s) R (and S) are not uniformly hashed:

    Use a different hash function (until you find a hash function that is uniform) Use a sort-based 2-pass algorithm