Improve performance of large sorts with Cascaded merge / tree
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Description
### Is your feature request related to a problem or challenge?
While working on https://github.com/apache/arrow-datafusion/pull/7179 I noticed a potential improvement
The key observation is that merging `K` sorted streams of total rows `N`:
1. takes time proportional to `O(N*K)`
2. is a single threaded operation
`K` is often called the "Fan In" of the merge
The implementation of [ExternalSorter::in_mem_sort_stream](https://github.com/apache/arrow-datafusion/blob/1e9816b07edd8e73bb45ababa20a7c22de492d96/datafusion/core/src/physical_plan/sorts/sort.rs#L259-L297) will effectively merge all the
buffered batches at once, as shown below. This can be a very large fan in -- 100s or 1000s of RecordBatches
```text
┌─────┐ ┌─────┐
│ 2 │ │ 1 │
│ 3 │ │ 2 │
│ 1 │─ ─▶ sort ─ ─▶│ 2 │─ ─ ─ ─ ─ ─ ┐
│ 4 │ │ 3 │
│ 2 │ │ 4 │ │
└─────┘ └─────┘
┌─────┐ ┌─────┐ │
│ 1 │ │ 1 │
│ 4 │─ ▶ sort ─ ─ ▶│ 1 ├ ─ ┐ │
│ 1 │ │ 4 │
└─────┘ └─────┘ │ │
... ... ▼
│
Could be 100s depending on ─ ─▶ merge ─ ─ ─ ─ ─▶ sorted output
the data being sorted stream
▲
... ...
┌─────┐ ┌─────┐ │
│ 3 │ │ 3 │
│ 1 │─ ▶ sort ─ ─ ▶│ 1 │─ ─ ─ ─ ─ ─ ┤
└─────┘ └─────┘
┌─────┐ ┌─────┐ │
│ 4 │ │ 3 │
│ 3 │─ ▶ sort ─ ─ ▶│ 4 │─ ─ ─ ─ ─ ─ ┘
└─────┘ └─────┘
in_mem_batches
```
### Describe the solution you'd like
A classical approach to such sorts is to use a "cascaded merge" which uses a series of merge operations each with a limited the fanout (e.g. to 10)
```
┌─────┐ ┌─────┐
│ 2 │ │ 1 │
│ 3 │ │ 2 │
│ 1 │─ ─▶ sort ─ ─▶│ 2 │─ ─ ─ ─ ─ ─ ─ ─ ┐
│ 4 │ │ 3 │
│ 2 │ │ 4 │ │
└─────┘ └─────┘
┌─────┐ ┌─────┐ ▼
│ 1 │ │ 1 │
│ 4 │─ ▶ sort ─ ─ ▶│ 1 ├ ─ ─ ─ ─ ─ ▶ merge ─ ─ ─ ─
│ 1 │ │ 4 │ │
└─────┘ └─────┘
... ... ... ▼
merge ─ ─ ─ ─ ─ ─ ▶ sorted output
stream
▲
... ... ... │
┌─────┐ ┌─────┐
│ 3 │ │ 3 │ │
│ 1 │─ ▶ sort ─ ─ ▶│ 1 │─ ─ ─ ─ ─ ─▶ merge ─ ─ ─ ─
└─────┘ └─────┘
┌─────┐ ┌─────┐ ▲
│ 4 │ │ 3 │
│ 3 │─ ▶ sort ─ ─ ▶│ 4 │─ ─ ─ ─ ─ ─ ─ ─ ┘
└─────┘ └─────┘
in_mem_batches do a series of merges that
each has a limited fan-in
(number of inputs)
```
This is often better because:
1. Is `O(N*ln(N)*ln(K))` , there is some additional overhead of `ln(N)` as the same row must now be compared several times
2. the intermediate merges can be run in parallel on multiple cores (though the final one is still single threaded)
It would be awesome if someone wanted to:
1. Verify the theory that there is a large fan in for large sorts
3. Implement a cascaded merge and measure if it improves performance
The sort [benchmark](https://github.com/apache/arrow-datafusion/tree/main/benchmarks) (TODO) (thanks @jaylmiller!) may be interesting:
```
cargo run --release --bin parquet -- sort --path ./data --scale-factor 1.0
```
### Describe alternatives you've considered
Another potential variation might be to get more cores involves in the merging by parallelizing the merge, as described in the [Morsel-Driven Parallelism paper](https://db.in.tum.de/~leis/papers/morsels.pdf)
### Additional context
_No response_
Contributor guide
Research direction
Start with ExternalSorter::in_mem_sort_stream in datafusion/core/src/physical_plan/sorts/sort.rs and verify how many buffered batches are merged for large sorts. Run the parquet benchmark with `cargo run --release --bin parquet -- sort --path ./data --scale-factor 1.0`, then implement and measure a cascaded merge; done means the fan-in and performance impact are documented by benchmark results.
Written by the indexing model from the issue text.
Assessment
- Tech stack
- rust
- Domain
- data-engineering, performance
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Mostly clear
- Newbie friendliness
- 35/100