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

• P1 send A to P2

• P2 compares B with A and sends to P1 the min(A,B)

Method 2

• P1 sends A to P2

• P2 sends B to P1

• P1 does A = min(A, B)

• P2 does B = max(A, B)

Data partitioning

– n numbers and p processors– n/p numbers assigned to each processorMethod 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.• a1 < a2 < . . . < ai−1 < ai > ai+1 > ai+2 > . . . > an

– 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 networkUnsorted sequence bitonic sequence sorted sequencehttps://www.youtube.com/watch?v=GEQ8y26blEY

Example

What’s next?

• Parallel computational geometry• Parallel numerical algorithms• …