Query Evaluation Styles

All-At-Once (Collections)

Bottom-up, one operator at a time.

Volcano-Style (Iterators)

Operators "request" one tuple at a time from children.

Push-Style (Buffers)

Operators continuously produce/consume tuples.

Analyzing Volcano Operators

• Memory Bounds
• Disk IO Used
• CPU Used

Databases are usually IO- or Memory-bound

Memory Bounds

• Constant
• Scales with output
• Scales with part of the input
• Worse

Core Question: Do we have enough memory to use this operator?

Disk IO

IO measured in:

• Number of Tuples
• Number of Data Pages (absolute size)

Table Scan ($R$)

Memory Required?

Constant!

IOs added?

$|R|$ tuples read

Select ($\sigma(R)$)

Select ($\sigma(R)$)

Memory Required?

Constant!

IOs added?

None! (Can "inline" into cost of $R$)

Project ($\pi(R)$)

Project ($\pi(R)$)

Memory Required?

Constant!

IOs added?

None!

Union ($R \cup S$)

Union ($R \cup S$)

Memory Required?

Constant!

IOs added?

None!

Cross ($R \times S$)

Cross ($R \times S$)

Memory Required?

Constant!

IOs added?

$(|R|-1) \cdot \texttt{cost}(S)$ tuples read

(or $(|S|-1) \cdot \texttt{cost}(R)$)

If $S$ is a query, this can get very expensive

Cross ($R \times S$)

Optimization 1: Cache $S$ in memory

Memory Required?

$O(|S|)$

IOs added?

None!

Cross ($R \times S$)

Optimization 2: Cache $S$ on disk

Memory Required?

Constant

IOs added?

$|S|$ tuples written.

$(|R| - 1) \cdot |R|$ tuples read.

Is there a middle ground?

Nested-Loop Join

Problem: We need to evaluate rhs iterator
once per record in lhs

Preloading Data

Better Solution: Load both lhs and rhs records in blocks.

                    def apply_cross(lhs, rhs):
                      result = []

                      while r_block = lhs.take(100):
                        while s_block = rhs.take(100):
                          for r in r_block:
                            for s in s_block: 
                              result += [r + s]
                        rhs.reset()

                      return result
    

Block-Nested Loop Join

Block-Nested Loop ($R \times S$)

(with $\mathcal B$ as the block size for $R$)

(and with caching $S$ to disk)

Memory Required?

$O(\mathcal B)$

IOs added?

$|S|$ tuples written.

$(\frac{|R|}{\mathcal B} - 1) \cdot |R|$ tuples read.

In-memory caching is a special case of block-nested loop with $\mathcal B = |S|$

Does the block size for $R$ matter?

How big should the blocks be?

Cross product is expensive!
Can we do better?

$\sigma_c(R\times S) \equiv R\bowtie_c S$

Cross Product

Problem: Naively, any tuple matches any other

Join Conditions

Solution: First organize the data

Strategies for Implementing $R \bowtie_{R.A = S.A} S$

In-Memory Index Join (1-pass Hash; Hash Join)

Build an in-memory index on one table, scan the other.

Partition Join (2-pass Hash; External Hash Join)

Partition both sides so that tuples don't join across partitions.

Sort/Merge Join

Sort all of the data upfront, then scan over both sides.

Hash Functions

• A hash function is a function that maps a large data value to a small fixed-size value
  • Typically is deterministic & pseudorandom
• Used in Checksums, Hash Tables, Partitioning, Bloom Filters, Caching, Cryptography, Password Storage, …
• Examples: MD5, SHA1, SHA2
  • MD5() part of OpenSSL (on most OSX / Linux / Unix)
• Can map h(k) to range [0,N) with h(k) % N (modulus)

Hash Functions

$$h(X) \mod N$$

• Pseudorandom output between $[0, N)$
• Always the same output for a given $X$

1-Pass Hash Join

1-Pass Hash Join

Limited Queries

Only supports join conditions of the form $R.A = S.B$

Moderate-High Memory

Keeps 1 full relation in memory

Low Added IO Cost

Only requires 1 scan over each input.

Alternative: Build an in-memory tree (e.g., B+Tree) instead of a hash table!

Limited Queries

Also supports $R.A \geq S.B$, $R.A > S.B$

Moderate-High Memory

Keeps 1 full relation in memory

Low Added IO Cost

Only requires 1 scan over each input.

2-Pass Hash Join

2-Pass Hash Join

Limited Queries

Only supports join conditions of the form $R.A = S.B$

Low Memory

Never need more than 1 pair of partitions in memory

High IO Cost

$|R| + |S|$ tuples written out

$|R| + |S|$ tuples read in

Why is it important that the hash function is pseudorandom?

What if the data is already organized (e.g., sorted) in a useful way?

Sort/Merge Join

Sort/Merge Join

Limited Queries

Only supports join conditions of the form $R.A = S.B$

Low Memory

Only needs to keep ~2 rows in memory at a time (not counting sort).

Low Added IO Cost

No added IO! (not counting sort).