tustvold commented on code in PR #264:
URL: https://github.com/apache/arrow-site/pull/264#discussion_r1014484528
##########
_posts/2022-10-30-multi-column-sorts-in-arrow-rust-part-1.md:
##########
@@ -0,0 +1,232 @@
+---
+layout: post
+title: "Fast and Memory Efficient Multi-Column Sorts in Apache Arrow Rust,
Part 1"
+date: "2022-10-30 00:00:00"
+author: "tustvold and alamb"
+categories: [arrow]
+---
+<!--
+{% comment %}
+Licensed to the Apache Software Foundation (ASF) under one or more
+contributor license agreements. See the NOTICE file distributed with
+this work for additional information regarding copyright ownership.
+The ASF licenses this file to you under the Apache License, Version 2.0
+(the "License"); you may not use this file except in compliance with
+the License. You may obtain a copy of the License at
+
+http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+{% endcomment %}
+-->
+
+## Introduction
+
+Sorting is one of the most fundamental operations in modern databases and
other analytic systems, underpinning important operators such as aggregates,
joins, window functions, merge, and more. By some estimates, more than half of
the execution time in data processing systems is spent sorting. Optimizing
sorts is therefore vital to improving query performance and overall system
efficiency.
+
+Sorting is also one of the most well studied topics in computer science. The
classic survey paper for databases is [Implementing Sorting in Database
Systems](https://dl.acm.org/doi/10.1145/1132960.1132964) by Goetz Graefe which
provides a thorough academic treatment and is still very applicable today.
However, it may not be obvious how to apply the wisdom and advanced techniques
described in that paper to modern systems. In addition, the excellent [DuckDB
blog on sorting](https://duckdb.org/2021/08/27/external-sorting.html)
highlights many sorting techniques, and mentions a comparable row format, but
it does not explain how to efficiently sort variable length strings or
dictionary encoded data.
+
+In this series we explain in detail the new [row
format](https://docs.rs/arrow/25.0.0/arrow/row/index.html) in the [Rust
implementation](https://github.com/apache/arrow-rs) of [Apache
Arrow](https://arrow.apache.org/), and how we used to make sorting more than
[3x](https://github.com/apache/arrow-rs/pull/2929) faster than an alternate
comparator based approach. The benefits are especially pronounced for strings,
dictionary encoded data, and sorts with large numbers of columns.
+
+
+## Multicolumn / Lexicographical Sort Problem
+
+Most languages have native, optimized operations to sort a single column
(array) of data, which are specialized based on the type of data being sorted.
The reason that sorting is typically more challenging in analytic systems is
that it must:
+
+1. Support multiple columns of data
+2. The column types are not knowable at compile time, and thus the compiler
can not typically generate optimized code.
+
+Multicolumn sorting is also referred to as lexicographical sorting in some
libraries.
+
+For example, given sales data for various customers and their state of
residence, a user might want to find the lowest 10 orders for each state.
+
+```text
+Customer | State | Orders
+—--------+-------+-------
+12345 | MA | 10.12
+532432 | MA | 8.44
+12345 | CA | 3.25
+56232 | WA | 6.00
+23442 | WA | 132.50
+7844 | CA | 9.33
+852353 | MA | 1.30
+```
+
+One way to do so is to order the data first by `State` and then by `Orders`:
+```text
+Customer | State | Orders
+—--------+-------+-------
+12345 | CA | 3.25
+7844 | CA | 9.33
+852353 | MA | 1.30
+532432 | MA | 8.44
+12345 | MA | 10.12
+56232 | WA | 6.00
+23442 | WA | 132.50
+```
+
+(Note: While there are specialized ways for computing this particular query
other than fully sorting the entire input (e.g. "TopK"), they typically need
the same multi-column comparison operation described below. Thus while we will
use the simplified example in our post, it applies much more broadly)
+
+## Basic Implementation
+
+Let us take the example of a basic sort kernel which takes a set of columns as
input, and returns a list of indices identifying a sorted order.
+
+```python
+> lexsort_to_indices([
+ ["MA", "MA", "CA", "WA", "WA", "CA", "MA"]
+ ])
+
+[2, 5, 0, 1, 6, 3, 4]
+
+> lexsort_to_indices([
+ ["MA", "MA", "CA", "WA", "WA", "CA", "MA"],
+ [10.10, 8.44, 3.25, 6.00, 132.50, 9.33, 1.30]
+ ])
+
+[2, 5, 6, 1, 0, 3, 4]
+```
+
+This function returns a list of indices instead of sorting the columns
directly because it:
+1. Avoids expensive copying data during the sorting process
+2. Allows deferring copying of values until the latest possible moment
+3. Can be used to reorder additional columns that weren’t part of the sort key
+
+
+A straightforward implementation of lexsort_to_indices uses a comparator
function,
+
+```text
+ row
+ index
+ ┌─────┐ ┌─────┐ ┌─────┐ compare(left_index, right_index)
+ 0 │ │ │ │ │ │
+ ┌├─────┤─ ─├─────┤─ ─├─────┤┐ │ │
+ │ │ │ │ │ │ ◀──────────────────┘ │
+ └├─────┤─ ─├─────┤─ ─├─────┤┘ │
+ │ │ │ │ │ │Comparator function compares one │
+ ├─────┤ ├─────┤ ├─────┤ multi-column row with another. │
+ │ │ │ │ │ │ │
+ ├─────┤ ├─────┤ ├─────┤ The data types of the columns │
+ │ │ │ │ │ │ and the sort options are not │
+ └─────┘ └─────┘ └─────┘ known at compile time, only │
+ ... runtime │
+ │
+ ┌┌─────┐─ ─┌─────┐─ ─┌─────┐┐ │
+ │ │ │ │ │ │ ◀────────────────────────────────┘
+ └├─────┤─ ─├─────┤─ ─├─────┤┘
+ │ │ │ │ │ │
+ ├─────┤ ├─────┤ ├─────┤
+ N-1 │ │ │ │ │ │
+ └─────┘ └─────┘ └─────┘
+ Customer State Orders
+ UInt64 Utf8 F64
+```
+
+
+The comparator function compares each row a column at a time, based on the
column types
+
+```text
+ ┌────────────────────────────────┐
+ │ │
+ ▼ │
+ ┌ ─ ─ ─ ┐ ┌ ─ ─ ─ ┐ │
+ │
+ ┌─────┐ │┌─────┐│ │┌─────┐│ │
+left_index │ │ │ │ │ │ │
+ └─────┘ │└─────┘│ │└─────┘│ Step 1: Compare State
+ (UInt64)
+ │ │ │ │
+
+ │ │ │ │
+ ┌─────┐ ┌─────┐ ┌─────┐
+ right_index│ │ ││ ││ ││ ││
+ └─────┘ └─────┘ └─────┘ Step 2: If State values equal
+ │ │ │ │ compare Orders (F64)
+ Customer State Orders │
+ UInt64 │ Utf8 │ │ F64 │ │
+ ─ ─ ─ ─ ─ ─ ─ ─ │
+ ▲ │
+ │ │
+ └───────────────────────┘
+```
+
+Pseudocode for this operation might look something like
+
+```python
+# Takes a list of columns and returns the lexicographically
+# sorted order as a list of indices
+def lexsort_to_indices(columns):
+ comparator = build_comparator(columns)
+
+ # Construct a list of integers from 0 to the number of rows
+ # and sort it according to the comparator
+ [0..columns.num_rows()].sort_by(comparator)
+
+# Build a function that given indexes (left_idx, right_idx)
+# returns the comparison of the sort keys at the left
+# and right indices respectively
+def build_comparator(columns):
+ def comparator(left_idx, right_idx):
+ for column in columns:
+ # call a compare function which performs
+ # dynamic dispatch on type of left and right columns
+ ordering = compare(column, left_idx,right_idx)
+ if ordering != Equal {
+ return ordering
+ }
+ # All values equal
+ Equal
+ # Return comparator function
+ comparator
+
+ # compares the values in a single column at left_idx and right_idx
+ def compare(column, left_idx, right_idx):
+ # Choose comparison based on type of column ("dynamic dispatch")
+ if column.type == Int:
+ cmp(column[left_idx].as_int(), column[right_idx].as_int())
+ elif column.type == Float:
+ cmp(column[left_idx].as_float(), column[right_idx].as_float())
+ ...
+```
+
+Greater detail is beyond the scope of this post, but in general the more
predictable the behavior of a block of code, the better its performance will
be. In the case of this pseudocode, there is clear room for improvement:
+
+1. `comparator` performs a large number of unpredictable conditional branches,
where the path execution takes depends on the data values
+2. `comparator` and `compare` use dynamic dispatch, which not only adds
further conditional branches, but also function call overhead
+3. `comparator` performs a large number of reads of memory at unpredictable
locations
+
+You can find the complete implementation of multi-column comparator
construction in arrow-rs in
[sort.rs](https://github.com/apache/arrow-rs/blob/f629a2ebe08033e7b78585d82e98c50a4439e7a2/arrow/src/compute/kernels/sort.rs#L905-L1036)
and
[ord.rs](https://github.com/apache/arrow-rs/blob/f629a2e/arrow/src/array/ord.rs#L178-L313).
+
+
+# Normalized Keys / Byte Array Comparisons
+
+Now imagine we had a way to represent each logical row of data as a sequence
of bytes, and that byte-wise comparison of that sequence yielded the same
result as comparing the actual column values using the code above. Such a
representation would require no switching on column types, and the kernel would
become
+
+```python
+def lexsort_to_indices(columns):
+ rows = convert_to_rows(columns)
+ [0..columns.num_rows()].sort_by(lambda l, r: cmp(rows[l], rows[r]))
+```
+
+While this approach does require converting to/from the byte array
representation, it has some major advantages:
+
+* Rows can be compared by comparing bytes in memory, which modern computer
hardware excels at with the extremely well optimized
[memcmp](https://www.man7.org/linux/man-pages/man3/memcmp.3.html)
+* Memory accesses are largely predictable
+* There is no dynamic dispatch overhead
+* Extends straightforwardly to more sophisticated sorting strategies such as
+ * Distribution-based sorting techniques such as radix sort
+ * Parallel merge sort
+ * External sort
+ * ...
+
+You can find more information on how to leverage such representation in the
"Binary String Comparison" section of the [DuckDB blog
post](https://duckdb.org/2021/08/27/external-sorting.html) on the topic as well
as [Graefe’s paper](https://dl.acm.org/doi/10.1145/1132960.1132964). However,
we found it wasn’t immediately obvious how to apply this technique to variable
length string or dictionary encoded data, which we will explain in the next
section of this article.
Review Comment:
```suggestion
You can find more information on how to leverage such representation in the
"Binary String Comparison" section of the [DuckDB blog
post](https://duckdb.org/2021/08/27/external-sorting.html) on the topic as well
as [Graefe’s paper](https://dl.acm.org/doi/10.1145/1132960.1132964). However,
we found it wasn’t immediately obvious how to apply this technique to variable
length string or dictionary encoded data, which we will explain in the next
post in this series.
```
##########
_posts/2022-10-30-multi-column-sorts-in-arrow-rust-part-1.md:
##########
@@ -0,0 +1,232 @@
+---
+layout: post
+title: "Fast and Memory Efficient Multi-Column Sorts in Apache Arrow Rust,
Part 1"
+date: "2022-10-30 00:00:00"
+author: "tustvold and alamb"
+categories: [arrow]
+---
+<!--
+{% comment %}
+Licensed to the Apache Software Foundation (ASF) under one or more
+contributor license agreements. See the NOTICE file distributed with
+this work for additional information regarding copyright ownership.
+The ASF licenses this file to you under the Apache License, Version 2.0
+(the "License"); you may not use this file except in compliance with
+the License. You may obtain a copy of the License at
+
+http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+{% endcomment %}
+-->
+
+## Introduction
+
+Sorting is one of the most fundamental operations in modern databases and
other analytic systems, underpinning important operators such as aggregates,
joins, window functions, merge, and more. By some estimates, more than half of
the execution time in data processing systems is spent sorting. Optimizing
sorts is therefore vital to improving query performance and overall system
efficiency.
+
+Sorting is also one of the most well studied topics in computer science. The
classic survey paper for databases is [Implementing Sorting in Database
Systems](https://dl.acm.org/doi/10.1145/1132960.1132964) by Goetz Graefe which
provides a thorough academic treatment and is still very applicable today.
However, it may not be obvious how to apply the wisdom and advanced techniques
described in that paper to modern systems. In addition, the excellent [DuckDB
blog on sorting](https://duckdb.org/2021/08/27/external-sorting.html)
highlights many sorting techniques, and mentions a comparable row format, but
it does not explain how to efficiently sort variable length strings or
dictionary encoded data.
+
+In this series we explain in detail the new [row
format](https://docs.rs/arrow/25.0.0/arrow/row/index.html) in the [Rust
implementation](https://github.com/apache/arrow-rs) of [Apache
Arrow](https://arrow.apache.org/), and how we used to make sorting more than
[3x](https://github.com/apache/arrow-rs/pull/2929) faster than an alternate
comparator based approach. The benefits are especially pronounced for strings,
dictionary encoded data, and sorts with large numbers of columns.
+
+
+## Multicolumn / Lexicographical Sort Problem
+
+Most languages have native, optimized operations to sort a single column
(array) of data, which are specialized based on the type of data being sorted.
The reason that sorting is typically more challenging in analytic systems is
that it must:
+
+1. Support multiple columns of data
+2. The column types are not knowable at compile time, and thus the compiler
can not typically generate optimized code.
+
+Multicolumn sorting is also referred to as lexicographical sorting in some
libraries.
+
+For example, given sales data for various customers and their state of
residence, a user might want to find the lowest 10 orders for each state.
+
+```text
+Customer | State | Orders
+—--------+-------+-------
+12345 | MA | 10.12
+532432 | MA | 8.44
+12345 | CA | 3.25
+56232 | WA | 6.00
+23442 | WA | 132.50
+7844 | CA | 9.33
+852353 | MA | 1.30
+```
+
+One way to do so is to order the data first by `State` and then by `Orders`:
+```text
+Customer | State | Orders
+—--------+-------+-------
+12345 | CA | 3.25
+7844 | CA | 9.33
+852353 | MA | 1.30
+532432 | MA | 8.44
+12345 | MA | 10.12
+56232 | WA | 6.00
+23442 | WA | 132.50
+```
+
+(Note: While there are specialized ways for computing this particular query
other than fully sorting the entire input (e.g. "TopK"), they typically need
the same multi-column comparison operation described below. Thus while we will
use the simplified example in our post, it applies much more broadly)
+
+## Basic Implementation
+
+Let us take the example of a basic sort kernel which takes a set of columns as
input, and returns a list of indices identifying a sorted order.
+
+```python
+> lexsort_to_indices([
+ ["MA", "MA", "CA", "WA", "WA", "CA", "MA"]
+ ])
+
+[2, 5, 0, 1, 6, 3, 4]
+
+> lexsort_to_indices([
+ ["MA", "MA", "CA", "WA", "WA", "CA", "MA"],
+ [10.10, 8.44, 3.25, 6.00, 132.50, 9.33, 1.30]
+ ])
+
+[2, 5, 6, 1, 0, 3, 4]
+```
+
+This function returns a list of indices instead of sorting the columns
directly because it:
+1. Avoids expensive copying data during the sorting process
+2. Allows deferring copying of values until the latest possible moment
+3. Can be used to reorder additional columns that weren’t part of the sort key
+
+
+A straightforward implementation of lexsort_to_indices uses a comparator
function,
+
+```text
+ row
+ index
+ ┌─────┐ ┌─────┐ ┌─────┐ compare(left_index, right_index)
+ 0 │ │ │ │ │ │
+ ┌├─────┤─ ─├─────┤─ ─├─────┤┐ │ │
+ │ │ │ │ │ │ ◀──────────────────┘ │
+ └├─────┤─ ─├─────┤─ ─├─────┤┘ │
+ │ │ │ │ │ │Comparator function compares one │
+ ├─────┤ ├─────┤ ├─────┤ multi-column row with another. │
+ │ │ │ │ │ │ │
+ ├─────┤ ├─────┤ ├─────┤ The data types of the columns │
+ │ │ │ │ │ │ and the sort options are not │
+ └─────┘ └─────┘ └─────┘ known at compile time, only │
+ ... runtime │
+ │
+ ┌┌─────┐─ ─┌─────┐─ ─┌─────┐┐ │
+ │ │ │ │ │ │ ◀────────────────────────────────┘
+ └├─────┤─ ─├─────┤─ ─├─────┤┘
+ │ │ │ │ │ │
+ ├─────┤ ├─────┤ ├─────┤
+ N-1 │ │ │ │ │ │
+ └─────┘ └─────┘ └─────┘
+ Customer State Orders
+ UInt64 Utf8 F64
+```
+
+
+The comparator function compares each row a column at a time, based on the
column types
+
+```text
+ ┌────────────────────────────────┐
+ │ │
+ ▼ │
+ ┌ ─ ─ ─ ┐ ┌ ─ ─ ─ ┐ │
+ │
+ ┌─────┐ │┌─────┐│ │┌─────┐│ │
+left_index │ │ │ │ │ │ │
+ └─────┘ │└─────┘│ │└─────┘│ Step 1: Compare State
+ (UInt64)
+ │ │ │ │
+
+ │ │ │ │
+ ┌─────┐ ┌─────┐ ┌─────┐
+ right_index│ │ ││ ││ ││ ││
+ └─────┘ └─────┘ └─────┘ Step 2: If State values equal
+ │ │ │ │ compare Orders (F64)
+ Customer State Orders │
+ UInt64 │ Utf8 │ │ F64 │ │
+ ─ ─ ─ ─ ─ ─ ─ ─ │
+ ▲ │
+ │ │
+ └───────────────────────┘
+```
+
+Pseudocode for this operation might look something like
+
+```python
+# Takes a list of columns and returns the lexicographically
+# sorted order as a list of indices
+def lexsort_to_indices(columns):
+ comparator = build_comparator(columns)
+
+ # Construct a list of integers from 0 to the number of rows
+ # and sort it according to the comparator
+ [0..columns.num_rows()].sort_by(comparator)
+
+# Build a function that given indexes (left_idx, right_idx)
+# returns the comparison of the sort keys at the left
+# and right indices respectively
+def build_comparator(columns):
+ def comparator(left_idx, right_idx):
+ for column in columns:
+ # call a compare function which performs
+ # dynamic dispatch on type of left and right columns
+ ordering = compare(column, left_idx,right_idx)
+ if ordering != Equal {
+ return ordering
+ }
+ # All values equal
+ Equal
+ # Return comparator function
+ comparator
+
+ # compares the values in a single column at left_idx and right_idx
+ def compare(column, left_idx, right_idx):
+ # Choose comparison based on type of column ("dynamic dispatch")
+ if column.type == Int:
+ cmp(column[left_idx].as_int(), column[right_idx].as_int())
+ elif column.type == Float:
+ cmp(column[left_idx].as_float(), column[right_idx].as_float())
+ ...
+```
+
+Greater detail is beyond the scope of this post, but in general the more
predictable the behavior of a block of code, the better its performance will
be. In the case of this pseudocode, there is clear room for improvement:
+
+1. `comparator` performs a large number of unpredictable conditional branches,
where the path execution takes depends on the data values
+2. `comparator` and `compare` use dynamic dispatch, which not only adds
further conditional branches, but also function call overhead
+3. `comparator` performs a large number of reads of memory at unpredictable
locations
+
+You can find the complete implementation of multi-column comparator
construction in arrow-rs in
[sort.rs](https://github.com/apache/arrow-rs/blob/f629a2ebe08033e7b78585d82e98c50a4439e7a2/arrow/src/compute/kernels/sort.rs#L905-L1036)
and
[ord.rs](https://github.com/apache/arrow-rs/blob/f629a2e/arrow/src/array/ord.rs#L178-L313).
+
+
+# Normalized Keys / Byte Array Comparisons
+
+Now imagine we had a way to represent each logical row of data as a sequence
of bytes, and that byte-wise comparison of that sequence yielded the same
result as comparing the actual column values using the code above. Such a
representation would require no switching on column types, and the kernel would
become
+
+```python
+def lexsort_to_indices(columns):
+ rows = convert_to_rows(columns)
+ [0..columns.num_rows()].sort_by(lambda l, r: cmp(rows[l], rows[r]))
+```
+
+While this approach does require converting to/from the byte array
representation, it has some major advantages:
+
+* Rows can be compared by comparing bytes in memory, which modern computer
hardware excels at with the extremely well optimized
[memcmp](https://www.man7.org/linux/man-pages/man3/memcmp.3.html)
+* Memory accesses are largely predictable
+* There is no dynamic dispatch overhead
+* Extends straightforwardly to more sophisticated sorting strategies such as
+ * Distribution-based sorting techniques such as radix sort
+ * Parallel merge sort
+ * External sort
+ * ...
+
+You can find more information on how to leverage such representation in the
"Binary String Comparison" section of the [DuckDB blog
post](https://duckdb.org/2021/08/27/external-sorting.html) on the topic as well
as [Graefe’s paper](https://dl.acm.org/doi/10.1145/1132960.1132964). However,
we found it wasn’t immediately obvious how to apply this technique to variable
length string or dictionary encoded data, which we will explain in the next
section of this article.
+
+
+## Next up: Row Format
+
+This post has introduced the concept and challenges of multi column sorting,
and shown why a comparable byte array representation, such as the [row
format](https://docs.rs/arrow/25.0.0/arrow/row/index.html) introduced to the
[Rust implementation](https://github.com/apache/arrow-rs) of [Apache
Arrow](https://arrow.apache.org/), is such a compelling primitive.
Review Comment:
```suggestion
This post has introduced the concept and challenges of multi column sorting,
and shown why a comparable byte array representation, such as the [row
format](https://docs.rs/arrow/25.0.0/arrow/row/index.html) introduced to the
[Rust implementation](https://github.com/apache/arrow-rs) of [Apache
Arrow](https://arrow.apache.org/), is such a compelling primitive.
```
##########
_posts/2022-10-30-multi-column-sorts-in-arrow-rust-part-1.md:
##########
@@ -0,0 +1,232 @@
+---
+layout: post
+title: "Fast and Memory Efficient Multi-Column Sorts in Apache Arrow Rust,
Part 1"
+date: "2022-10-30 00:00:00"
+author: "tustvold and alamb"
+categories: [arrow]
+---
+<!--
+{% comment %}
+Licensed to the Apache Software Foundation (ASF) under one or more
+contributor license agreements. See the NOTICE file distributed with
+this work for additional information regarding copyright ownership.
+The ASF licenses this file to you under the Apache License, Version 2.0
+(the "License"); you may not use this file except in compliance with
+the License. You may obtain a copy of the License at
+
+http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+{% endcomment %}
+-->
+
+## Introduction
+
+Sorting is one of the most fundamental operations in modern databases and
other analytic systems, underpinning important operators such as aggregates,
joins, window functions, merge, and more. By some estimates, more than half of
the execution time in data processing systems is spent sorting. Optimizing
sorts is therefore vital to improving query performance and overall system
efficiency.
+
+Sorting is also one of the most well studied topics in computer science. The
classic survey paper for databases is [Implementing Sorting in Database
Systems](https://dl.acm.org/doi/10.1145/1132960.1132964) by Goetz Graefe which
provides a thorough academic treatment and is still very applicable today.
However, it may not be obvious how to apply the wisdom and advanced techniques
described in that paper to modern systems. In addition, the excellent [DuckDB
blog on sorting](https://duckdb.org/2021/08/27/external-sorting.html)
highlights many sorting techniques, and mentions a comparable row format, but
it does not explain how to efficiently sort variable length strings or
dictionary encoded data.
+
+In this series we explain in detail the new [row
format](https://docs.rs/arrow/25.0.0/arrow/row/index.html) in the [Rust
implementation](https://github.com/apache/arrow-rs) of [Apache
Arrow](https://arrow.apache.org/), and how we used to make sorting more than
[3x](https://github.com/apache/arrow-rs/pull/2929) faster than an alternate
comparator based approach. The benefits are especially pronounced for strings,
dictionary encoded data, and sorts with large numbers of columns.
+
+
+## Multicolumn / Lexicographical Sort Problem
+
+Most languages have native, optimized operations to sort a single column
(array) of data, which are specialized based on the type of data being sorted.
The reason that sorting is typically more challenging in analytic systems is
that it must:
+
+1. Support multiple columns of data
+2. The column types are not knowable at compile time, and thus the compiler
can not typically generate optimized code.
+
+Multicolumn sorting is also referred to as lexicographical sorting in some
libraries.
+
+For example, given sales data for various customers and their state of
residence, a user might want to find the lowest 10 orders for each state.
+
+```text
+Customer | State | Orders
+—--------+-------+-------
+12345 | MA | 10.12
+532432 | MA | 8.44
+12345 | CA | 3.25
+56232 | WA | 6.00
+23442 | WA | 132.50
+7844 | CA | 9.33
+852353 | MA | 1.30
+```
+
+One way to do so is to order the data first by `State` and then by `Orders`:
+```text
+Customer | State | Orders
+—--------+-------+-------
+12345 | CA | 3.25
+7844 | CA | 9.33
+852353 | MA | 1.30
+532432 | MA | 8.44
+12345 | MA | 10.12
+56232 | WA | 6.00
+23442 | WA | 132.50
+```
+
+(Note: While there are specialized ways for computing this particular query
other than fully sorting the entire input (e.g. "TopK"), they typically need
the same multi-column comparison operation described below. Thus while we will
use the simplified example in our post, it applies much more broadly)
Review Comment:
```suggestion
(Note: While there are specialized ways for computing this particular query
other than fully sorting the entire input (e.g. "TopK"), they typically need
the same multi-column comparison operation described below. Thus while we will
use the simplified example in this post, it applies much more broadly)
```
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