Sorting Algos in parallel system

8/6/2019 Sorting Algos in parallel system

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Sorting Algorithms in

Parallel Systems



Parallel Systems

Parallel Processing is information processing that

emphasizes the concurrent manipulation of data

elements belonging to one or more processes

solving a single problem.

A parallel computer is a multiple processor

computer capable of parallel processing.

It increases speed of execution.



Odd-Even (Transposition) Sort

� Its a variant of bubble sort.

� The algo performs N/2 iterations

� It has 2 phases :

E

ven-odd exchange

Odd even exchange



Odd-Even Algo



Odd-Even



Odd-Even Transposition

�After n phases of odd-even exchanges, the sequence

is sorted.

�Each phase of the algorithm (either odd or even)

requires (n) comparisons.

�Serial complexity is (n2).



Parallel Odd-Even Transposition



9

Parallel odd even transposition



9

Parallel odd even transposition

P0 P1 P2 P3

13 7 12 8 5 4 6 1 3 9 2 10

Local sort

7 12 13 4 5 8 1 3 6 2 9 10

O-E

4 5 7 8 12 13 1 2 3 6 9 10

E-O

4 5 7 1 2 3 8 12 13 6 9 10

O-E

1 2 3 4 5 7 6 8 9 10 12 13

E-O

SORTED: 1 2 3 4 5 6 7 8 9 10 12 13



Properties

� The parallel run time of the formulation is

�The efficiency is :

E=1 / [1 o( ( log p ) / ( log n ) ) + o(p / log n ) ]

� The parallel formulation is cost-optimal for p =

O(log n).

� The isoefficiency function of this parallel

formulation is ( p2 p).



Quick Sort

Quick sort is one of the most common sortingalgorithms because of its simplicity, low overhead, and

optimal average complexity.

Quick sort selects one of the entries in the sequence to

be the pivot and divides the sequence into two - one

with all elements less than the pivot and other greater.

The process is recursively applied to each of the sub

lists.



Quick Sort



Quick Sort

Example of quick sort algorithm sorting asequence of size n = 8.



ParallelizingQuick Sort

�Executing a quick sort can be visualized by constructing a binary tree.

�We select a pivot. Partition the array into 2 parts:

a) Left ( Smaller ) .

b) Right ( Larger).

�The formulation does not rearrange the elements .

�All the processes can read the pivot in const time .Henceknow which sub-array( smaller or larger) is assigned to it and

proceed to next iteration.




� A binary tree generated by theexecution of the quick sortalgorithm.

� Each level of the treerepresents a different array-partitioning iteration.

� If pivot selection is optimal,then the height of the tree is(log n), which is also thenumber of iterations.




� Consider a list of size n equally divided across pprocessors.

� A pivot is selected by one of the processors and made

known to all processors.

� Each processor partitions its list into two sub array, say

Liand U

i, based on the selected pivot.

� All of the Li lists are merged and all of the U i lists aremerged separately.




� The set of processors is partitioned into two(in proportion of the size of lists L and U ). Theprocess is recursively applied to each of thelists.

� The recursion ends when a particular sub-block of element is assigned to a singleprocess.

� The processor than sorts than sorts theelements using a serial quick sort algo.



Parallelizing Quick Sort





Parallelizing Quick Sort

Therefore, the total parallel time is:

The corresponding isoefficiency is ( plog2 p) due to broadcast and

scan operations.





Conclusion

� In every real time systems we need to have

sorting.

� Sorted data is always easy to manipulate

than random data.



Thank you

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Sorting Algos in parallel system