This document discusses using SIMD (Single Instruction Multiple Data) instructions to parallelize dynamic programming algorithms. It provides an example of how a SIMD register can execute the same operation on multiple data elements in parallel. It also describes how to partition the dynamic programming problem into properly aligned chunks that can be processed simultaneously using SIMD to improve performance. Boundary conditions and dependencies between chunks are identified as challenges to be addressed for an effective parallel implementation.

1. Dynamic Programming on SIMD

2. SIMD (SSE)
A register has say Example
4 parts, each x:=x+y
part has 8 bits or
16 bits
x,y are memory locations of
Each part appropriate alignment and
executes the each refers to 4 different
same operation variables
but in parallel

3. Edit Distance between Strings
Q
D
Edit distance
between Q[1..j]
and D[1..i]

4. E(i,j)

5. F(i,j)

6. Summarizing
A G C T
A -1 2 2 2
G 2 -1 2 2
C 2 2 -1 2
T 2 2 2 -1

7. Parallel Computing
Find the max
value path from
Mismatch
each location to
the top left
corner
Insertion in
Q
Insertion in
D

8. Parallel Computing
Anti-
diagonal
can be
done in
parallel

9. SIMD?
One SIMD register
can handle all
values in this chunk
Partition into
chunks, each chunk
should have proper
alignment

10. Fix: Go Vertical
Partition into vertical
chunks, each chunk
should have proper
alignment

11. Problem 1: Boundaries
One value comes from
the previous chunk
Each chunk needs a
shift

12. Solution 1: Striping
x’s belong to one
chunk, y’s to another
and so on

13. Problem 2: Computing F
At most number of
blocks
Sequential Dependency

14. Problem 2: Computing F
Sequential Dependency

15. Thank You