1. Data Structures and Algorithms in Parallel Computing Lecture 8

2. 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)

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

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

5. 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)

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

7. Data partitioning Method 2

8. Algorithms Bubblesort Mergesort Quicksort Bitonic sort

9. Sequential bubblesort

10. Parallel bubblesort Run multiple iterations in parallel

11. Parallel mergesort Divide and conquer technique

12. Parallel quicksort

13. 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.

14. Bitonic sorting network Unsorted sequence  bitonic sequence  sorted sequence https://www.youtube.com/watch?v=GEQ8y26blEY

15. Example

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