SQL Join Algorithm

• Notations:
  • $[T]$: Number of pages in table T
  • ${\rho }_T$: The number of records on each page of T
  • $|T|$: The total number of records in table T, $|T|=[T]\times {\rho }_T$

Nested Loop Join

Simple Nested Loop Join

• Input Output Count: $[R]+|R|[S]$
  

Page Nested Loop Join

• Input Output Count: $[R]+[R][S]$
  • $S$ should be the smaller table to minimize the Input Output cost.
• Read in every single page in $S$ for every single page of $R$
• A special case of block nested loop join with $B=3$
  

Block Nested Loop Join

We have $B$ buffer pages to spare, give $B-2$ pages to $R$ and match $S$ against every record in the buffer.

• Input Output Count: $[R]+\frac{[R]}{B-2}[S]$
  

Hash Join

• Key Skew: many of the records have the same key. Cause some bucket much larger than others, leading to performance issues in join algorithms that rely on hash tables.

Grace Hash Join

• Idea: partitioning the input relations into smaller subsets, hashing each subset, and then joining the hashed partitions.
• Procedures: Repeatedly hash $R$ and $S$ into $B-1$ buffers so that we can get partitions that are $\le B-2$ pages big.
• Notes: sensitive to key skew.

Sort Merge Join

• Input Output Count: Cost to sort $R$ and $S$ $+([R]+[S])$
• External Sort
  • Merge Sort
• If first input is smaller than second input, advance
• advance second input till end
• advance first input till end
  

Links

• Category:Join algorithms - Wikipedia
• Hashtable