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One-pass Algorithm for ∪_B

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Slideshow:

The bag union (∪_B) operator

Note: ∪_B simply concatenates the inputs
The one-pass bag union (∪_B) algorithm

Buffer allocation
How to assign buffers when there are M buffers available:
   
We can re-use the M buffers for the second input relation (S)
IO cost and buffer requirement for ∪_B
 
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• Bag Union ∪_B
  • Bag Union operator:

    R ∪B S

  • Example Bag Union:

    R = {1, 2, 3}; S = {2, 3, 4}; R ∪B S = { 1, 2, 3, 2, 3, 4}

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  • One-pass algorithm:

    while ( R has more data blocks ) { read data blocks to fill available buffer; Move qualifying tuples to output } while ( S has more data blocks ) { read data blocks to fill available buffer; Move qualifying tuples to output }

    Buffer utilization when there are M buffers available:

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• Cost Analysis for ∪
  • # disk I/O used:

    B(R) + B(S) --- if the relations R and S are clustered T(R) + T(S) --- if the relations R and S is UNclustered

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  • Memory requirement:

    M ≥ 1 buffer