scandum / cubesort

A stable adaptive partitioning comparison sort.

Intro

This document describes a stable partitioning comparison sort named cubesort.

Binary Cube

Cubesort sorts data by storing data in a binary cube, a multidimentional balanced array.

Binary Search

In order to sort 1 element, 3 monobound binary searches are performed to pin point the bucket where the element should be stored.

Overflow

Once a bucket overflows it is sorted by quadsort and the content is split between two buckets.

Finish

Once all elements have been inserted into the cube, all unsorted buckets are sorted. Since the buckets are already in order the sort is finished.

Big O

Name	Best	Average	Worst	Stable	Partitioning	Memory
cubesort	n	n log n	n log n	yes	yes	n

Cubesort makes n comparisons when the data is already sorted or reverse sorted.

Benchmarks

The following benchmark was on WSL gcc version 7.4.0 (Ubuntu 7.4.0-1ubuntu1~18.04.1). The source code was compiled using g++ -O3 -w -fpermissive bench.c. Each test was ran 100 times and only the best run is reported.

Name	Items	Type	Best	Average	Repetitions	Distribution
std::sort	100000	i32	0.005530	0.005565	1	random order
cubesort	100000	i32	0.004708	0.004736	1	random order
std::sort	100000	i32	0.000943	0.001046	1	ascending order
cubesort	100000	i32	0.000275	0.000280	1	ascending order
std::sort	100000	i32	0.003193	0.003216	1	ascending saw
cubesort	100000	i32	0.001570	0.001583	1	ascending saw
std::sort	100000	i32	0.002931	0.002965	1	generic order
cubesort	100000	i32	0.001830	0.001851	1	generic order
std::sort	100000	i32	0.000739	0.000774	1	descending order
cubesort	100000	i32	0.000251	0.000257	1	descending order
std::sort	100000	i32	0.002765	0.002775	1	descending saw
cubesort	100000	i32	0.001139	0.001200	1	descending saw
std::sort	100000	i32	0.003713	0.003729	1	random tail
cubesort	100000	i32	0.001385	0.001398	1	random tail
std::sort	100000	i32	0.004755	0.004782	1	random half
cubesort	100000	i32	0.002541	0.002558	1	random half

Source code

Coming soon-ish.