The document discusses bubble sort and parallel sorting algorithms. It begins with an example of bubble sort, which iteratively compares adjacent elements and swaps them if they are in the wrong order. Next, it considers parallelizing bubble sort but notes some operations cannot be parallelized. Then it introduces Odd-Even Transposition Sort (OETS), which can sort in parallel by sorting odd and even indices independently in each round. With p processing threads, OETS has complexity of O(n/p * n), making it linearly scalable.

1. by Cristian Chilipirea
9 6 9 4 2 7 6 5 6 1
Bubble sort
6 9 9 4 2 7 6 5 6 1
6 9 9 4 2 7 6 5 6 1
6 9 4 9 2 7 6 5 6 1
6 9 4 2 9 7 6 5 6 1

2. by Cristian Chilipirea
6 9 4 2 7 9 6 5 6 1
Bubble sort
6 9 4 2 7 6 9 5 6 1
6 9 4 2 7 6 5 9 6 1
6 9 4 2 7 6 5 6 9 1
6 9 4 2 7 6 5 6 1 9
Repeat
until
sorted

3. by Cristian Chilipirea
6 9 4 2 7 6 5 6 1 9
Bubble sort
6 4 9 2 7 6 5 6 1 9
6 4 2 9 7 6 5 6 1 9
6 4 2 7 9 6 5 6 1 9
6 4 2 7 6 9 5 6 1 9

4. by Cristian Chilipirea
6 4 2 7 6 5 9 6 1 9
Bubble sort
6 4 2 7 6 5 6 9 1 9
6 4 2 7 6 5 6 1 9 9
6 4 2 7 6 5 6 1 9 9
……….

5. Complexity: O(𝒏 𝟐
)
It goes through all elements
Guaranteed to sort in n repetitions
Named bubble because large elements raise to the surface
(similar to bubbles in sparkling water)
by Cristian Chilipirea
Bubble sort
1 2 4 5 6 6 6 7 9 9
……….
4 6 2 7 6 5 6 1 9 9

6. by Cristian Chilipirea
9 6 9 4 2 7 6 5 6 1
Parallel bubble sort
6 9 9 4 2 7 6 5 6 1
These two operations (and all pairs like them)
cannot be executed in parallel

7. by Cristian Chilipirea
9 6 9 4 2 7 6 5 6 1
Parallel bubble sort
6 9 9 4 2 7 6 5 6 1
These two operations (and all pairs like them)
cannot be executed in parallel
Solution hint: The operations do not need
to be executed in exactly the same order

8. by Cristian Chilipirea
9 6 9 4 2 7 6 5 6 1
OETS: Odd-Even Transposition Sort
9 6 9 4 2 7 6 5 6 1
Repeat until
sorted
(maximum n
times
guarantee)

9. by Cristian Chilipirea
9 6 9 4 2 7 6 5 6 1
OETS: Odd-Even Transposition Sort
9 6 9 4 2 7 6 5 6 1
………..
………..
Can be
executed
in parallel
Can be
executed
in parallel
………..

10. by Cristian Chilipirea
9 6 9 4 2 7 6 5 6 1
OETS: Odd-Even Transposition Sort
9 6 9 4 2 7 6 5 6 1
………..
………..
………..
Can NOT be
executed
in parallel

11. by Cristian Chilipirea
9 6 9 4 2 7 6 5 6 1
OETS: Odd-Even Transposition Sort
9 6 9 4 2 7 6 5 6 1
………..
………..
………..
Solution:
Barrier
between
each
iteration

12. by Cristian Chilipirea
9 6 9 4 2 7 6 5 6 1
OETS: Odd-Even Transposition Sort
9 6 9 4 2 7 6 5 6 1
………..
………..
………..
Parallel complexity:
p = threads or
processor cores
O(
𝑛
𝑝
∗ 𝑛) = O(𝑛) for p=n

13. by Cristian Chilipirea
9 6 9 4 2 7 6 5 6 1
OETS: Odd-Even Transposition Sort
6 9 4 9 2 7 5 6 1 6
6 4 9 2 9 5 7 1 6 6
4 6 2 9 5 9 1 7 6 6

14. by Cristian Chilipirea
OETS: Odd-Even Transposition Sort
4 2 6 5 9 1 9 6 7 6
2 4 5 6 1 9 6 9 6 7
2 4 5 1 6 6 9 6 9 7
2 4 1 5 6 6 6 9 7 9

15. by Cristian Chilipirea
OETS: Odd-Even Transposition Sort
2 1 4 5 6 6 6 7 9 9
1 2 4 5 6 6 6 7 9 9
1 2 4 5 6 6 6 7 9 9
1 2 4 5 6 6 6 7 9 9