This Week

• Homework 03 Due Today
• Final Project group & topic selection, also due Today
  • Option 1: computing prime numbers
  • Option 2: sorting
  • Option 3: choose your own adventure

Sorting

The Task

Input. A (large) array float[] values

Task. Modify values so that the values are increasing.

Scale. values.length = 1_048_576 ($= 2^{20}$)

Baseline. Arrays.sort(values)

• include java.util.Arrays

Sorting by Divide-and-Conquer

General Strategy:

• break problem up into smaller sub-tasks
• solve sub-tasks
• combine sub-solutions to get total solution

Question 1. How to divide sorting problem?

Strategy 1: Divide by Index

Idea. (merge sort)

1. Split array into left and right sub-arrays
2. Sort left and right
3. Merge sorted left and right

Example. Sort [4, 2, 3, 1]

Parallelism?

Question. What can be performed in parallel?

1. Split array into left and right sub-arrays
2. Sort left and right
3. Merge sorted left and right

Strategy 2: Divide by Value

Idea. (quick sort)

1. Select a value pivot from array
2. Partition array into left and right sub-arrays
   • values in left are <= pivot, values in right are >
3. Sort left and right

Example. Sort [4, 2, 3, 1]

Parallelism?

Question. What can be performed in parallel?

1. Select a value pivot from array
2. Partition array into left and right sub-arrays
   • values in left are <= pivot, values in right are >
3. Sort left and right

(Dis)advantages?

Merge sort: split, sub-sort, merge

When to Stop Recursing?

Merge Sort?

Merge Operation

Question. How to merge two sorted arrays?

Speeding Up Merge?

Question. Can we improve performance of merge operation with SIMD instructions?

Partition Operation?

Question. How to partition an array given a pivot?

Speeding Up Partition?

Question. Can we improve performance of partition with SIMD instructions?

Next Week

1. Fork-join pools: thread pools tailored to recursive methods!
2. Sorting networks: the art of sorting small arrays