Data Structures and Algorithms in Parallel Computing Lecture 8

Parallel sorting Sorting is a problem that admits a variety of parallel solutions Goal – Sorting a sequence of values in increasing order using n processors Why in parallel? – Frequent operation in many applications – Best sequential algorithm is O(n log n) – In parallel on n processors we can aim for O(log n)

Compare and swap with message exchange Sequential version requires comparing and swapping values Parallel version requires an extra communication step

Method 1 P 1 send A to P 2 P 2 compares B with A and sends to P 1 the min(A,B)

Method 2 P 1 sends A to P 2 P 2 sends B to P 1 P 1 does A = min(A, B) P 2 does B = max(A, B)

Data partitioning – n numbers and p processors – n/p numbers assigned to each processor Method 1

Data partitioning Method 2

Algorithms Bubblesort Mergesort Quicksort Bitonic sort

Sequential bubblesort

Parallel bubblesort Run multiple iterations in parallel

Parallel mergesort Divide and conquer technique

Parallel quicksort

Bitonic sort Bitonic sequences – complexity: O(log 2n) – a sequence is bitonic if it contains two sequences, one increasing and one decreasing, i.e. a 1 a i+1 > a i+2 >... > a n – for some i such that (0 ≤ i ≤ n) – a sequence is bitonic if the property described is attained by a circular rotation to the right of its elements.

Bitonic sorting network Unsorted sequence  bitonic sequence  sorted sequence

Example

What’s next? Parallel computational geometry Parallel numerical algorithms …