GitHub issue #2122: Fast table queries with interpolation search
State: closed | Created: 2021-03-26T18:09:20Z

## Intro

This should fix issue #1803 

Currently querying examples in a dataset is O(n) because of the underlying pyarrow ChunkedArrays implementation.
To fix this I implemented interpolation search that is pretty effective since datasets usually verifies the condition of evenly distributed chunks (the default chunk size is fixed).

## Benchmark

Here is a [benchmark](https://pastebin.com/utEXUqsR) I did on bookcorpus (74M rows):

for the current implementation
```python
>>> python speed.py
Loaded dataset 'bookcorpus', len=74004228, nbytes=4835358766


========================= Querying unshuffled bookcorpus =========================

Avg access time key=1                                                 : 0.018ms
Avg access time key=74004227                                          : 0.215ms
Avg access time key=range(74003204, 74004228)                         : 1.416ms
Avg access time key=RandIter(low=0, high=74004228, size=1024, seed=42): 92.532ms

========================== Querying shuffled bookcorpus ==========================

Avg access time key=1                                                 : 0.187ms
Avg access time key=74004227                                          : 6.642ms
Avg access time key=range(74003204, 74004228)                         : 90.941ms
Avg access time key=RandIter(low=0, high=74004228, size=1024, seed=42): 3448.456ms
```

for the new one using interpolation search:
```python
>>> python speed.py
Loaded dataset 'bookcorpus', len=74004228, nbytes=4835358766


========================= Querying unshuffled bookcorpus =========================

Avg access time key=1                                                 : 0.076ms
Avg access time key=74004227                                          : 0.056ms
Avg access time key=range(74003204, 74004228)                         : 1.807ms
Avg access time key=RandIter(low=0, high=74004228, size=1024, seed=42): 24.028ms

========================== Querying shuffled bookcorpus ==========================

Avg access time key=1                                                 : 0.061ms
Avg access time key=74004227                                          : 0.058ms
Avg access time key=range(74003204, 74004228)                         : 22.166ms
Avg access time key=RandIter(low=0, high=74004228, size=1024, seed=42): 42.757ms
```

The RandIter class is just an iterable of 1024 random indices from 0 to 74004228.

Here is also a plot showing the speed improvement depending on the dataset size:
![image](https://user-images.githubusercontent.com/42851186/112673587-32335c80-8e65-11eb-9a0c-58ad774abaec.png)

## Implementation details:
- `datasets.table.Table` objects implement interpolation search for the `slice` method
- The interpolation search requires to store the offsets of all the chunks of a table. The offsets are stored when the `Table` is initialized.
- `datasets.table.Table.slice` returns a `datasets.table.Table` using interpolation search
- `datasets.table.Table.fast_slice` returns a `pyarrow.Table` object using interpolation search. This is useful to get a part of a dataset if we don't need the indexing structure for future computations. For example it's used when querying an example as a dictionary.
- Now a `Dataset` object is always backed by a `datasets.table.Table` object. If one passes a `pyarrow.Table` to initialize a `Dataset`, then it's converted to a `datasets.table.Table`

## Checklist:

- [x] implement interpolation search
- [x] use `datasets.table.Table` in `Dataset` objects
- [x] update current tests
- [x] add tests for interpolation search
- [x] comments and docstring
- [x] add the benchmark to the CI

Fix #1803.