1. Optimal Sorting Algorithms for Parallel Computers
CS300 - Technical Paper Review
Palash Chauhan (13455)

2. PROBLEM
Sort a sequence of n elements on a parallel computer with k processors.

3. Solution : Why is it interesting?
Studies done in parallel sorting prior to the paper equated the number of elements to be sorted with the number of processors and concluded that the speed-up was logarithmic in the number of processors. No algorithm with a linear speed-up was known.

4. Solution : Assumptions
The machine is composed of k processors (P1, P2..Pk) and each processor Pi has its own memory Mi which can be directly accessed by Pi .
A special instruction, the route instruction, allows the processor Pi to read one cell of the memory of an adjacent processor and store its contents in its own memory.
Each processor has the capability of inhibiting the execution of the current instruction by setting an appropriate indicator.

5. Solution : Central Idea
Given any algorithm which uses comparision-exchanges for sorting k elements with k processors, there is a corresponding algorithm for sorting rk elements with k processors where every comparision in the 1st algorithm is replaced by a merge-sorting two ordered lists of r elements in the 2nd.

6. Habermann’s Neighbourhood Sort
3,2,4,1 - P1 - 2,3,4,1
2,3,4,1 - P3 - 2,3,1,4
2,3,1,4 - P2 - 2,1,3,4
2,1,3,4 - P1 - 1,2,3,4

7. Solution : Algorithm

8. Comments
The assumptions are not restrictive. A real life parallel computer “Illiac IV” has those properties.
The implementation and the analysis of the algorithm are clearly explained.
The paper is easy to understand.

9. THANK YOU !