Bitonic sorter

Bitonic sorter

Bitonic sort network with eight inputs.
Class	Sorting algorithm
Data structure	Array
Worst-case performance	${\displaystyle O(\log ^{2}(n))}$ parallel time
Best-case performance	${\displaystyle O(\log ^{2}(n))}$ parallel time
Average performance	${\displaystyle O(\log ^{2}(n))}$ parallel time
Worst-case space complexity	${\displaystyle O(n\log ^{2}(n))}$ non-parallel time
Optimal	No

Bitonic mergesort is a parallel algorithm for sorting. It is also used as a construction method for building a sorting network. The algorithm was devised by Ken Batcher. The resulting sorting networks consist of ${\displaystyle O(n\log ^{2}(n))}$ comparators and have a delay of ${\displaystyle O(\log ^{2}(n))}$, where ${\displaystyle n}$ is the number of items to be sorted. This makes it a popular choice for sorting large numbers of elements on an architecture which itself contains a large number of parallel execution units running in lockstep, such as a typical GPU.

A sorted sequence is a monotonically non-decreasing (or non-increasing) sequence. A bitonic sequence is a sequence with ${\displaystyle x_{0}\leq \cdots \leq x_{k}\geq \cdots \geq x_{n-1}}$ for some ${\displaystyle k,0\leq k<n}$, or a circular shift of such a sequence.