This document describes sequential and parallel quicksort algorithms. Sequential quicksort has average complexity of O(n log n) but worst case of O(n^2). Parallel quicksort partitions the array, sorts subarrays in parallel threads, and waits for threads to complete to improve performance over sequential quicksort. It uses a queue to store threads if processors are busy and chooses split keys through various methods like first element or median. New threads are only created if the subarray size is above a minimum to reduce overhead.

1. Parallel quicksort
Sylwia Dzikiewicz
Marta Leniewska
Mikołaj Olszewski
Marcin Woch
Michał Żelazowski

2. Sequential quicksort
 Quicksort
(Array, start, end)
If (start < end)
middle = partition (Array, start, end)
quicksort(Array, start, middle)
quicksort(Array, middle+1, end)

3. Sequential quicksort
 Partition
(Array, start, end)
X = Array [start]
I = start - 1
J = end + 1
while TRUE
repeat J = J –1 until Array [ J ] <= X
repeat I = I +1 until Array [ I ] >=X
if I < J swap (Array [ I ], Array [ J ] )
else return J

4. Sequential quicksort – complexity
analysis
 Pessimistic
–
O (n2)
 Average
–
complexity
complexity
O (n log n)

5. Parallel quicksort
P a r a lle l q u ic k s o rt
Q s o rt
Q s o rt
Q s o rt
Q s o rt
Q s o rt
Q s o rt
Q s o rt
Q s o rt
Q s o rt
Q s o rt
Q s o rt

6. Parallel quicksort

How a single processor makes QuickSort (Array, start,
end)
–
–
–
–
–
J = Partition (Array, start, end)
Start a new thread on another processor : QuickSort(Array,
start, J)
Start a new thread on another processor : QuickSort(Array,
J+1, end)
Wait for both threads to complete
Notice your parent that your task is finished

7. Parallel quicksort
 OR
–
–
–
–
–
:
J = Partition (Array, start, end)
Start a new thread on another processor :
QuickSort(Array, start, J)
Execute QuickSort(Array, J+1, end)
Wait for the thread to complete
Notice your parent that your task is finished

8. Parallel quicksort
 In
case no processor can take thread, the
thread is put into a queue for later processing.
 After a processor has done its task, it checks
whether the queue contains any waiting
threads. If so, it removes the first task from the
queue and processes it.

9. Parallel quicksort
 Methods
–
–
–
of choosing the split key
First element
Average of : first, last and medium element
Median (the median of a sample is expected to be
the median of the whole array)

10. Parallel quicksort
A
new thread is created only if the length of the
array to sort is no less than MIN_ARRAY_SIZE
constant
 If the length of the array to sort is less than
MIN_QUICKSORT_SIZE, the array is sorted
using a simple algorithm (eg. Insertionsort or
Selectionsort), which require no new threads.
 MIN_QUICKSORT_SIZE <=
MIN_ARRAY_SIZE