# Parallel Algorithms - PowerPoint PPT Presentation

PPT – Parallel Algorithms PowerPoint presentation | free to download - id: 9f49e-NjljZ

The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
Title:

## Parallel Algorithms

Description:

### A Pram Algorithm. Every Processor knows its own index (usually indicated by variable i) ... Optimal Parallel Algorithms. NC -- The class of algorithms that run ... – PowerPoint PPT presentation

Number of Views:308
Avg rating:3.0/5.0
Slides: 18
Provided by: peterm8
Category:
Tags:
Transcript and Presenter's Notes

Title: Parallel Algorithms

1
Parallel Algorithms
2
Parallel Models
• Hypercube
• Butterfly
• Fully Connected
• Other Networks
• Shared Memory v.s. Distributed Memory
• SIMD v.s. MIMD

3
The PRAM Model
• Parallel Random Access Machine
• All processors act in lock-step
• Number of processors is not limited
• All processors have local memory
• One global memory accessible to all processors
• Processors must read and write global memory

4
A Pram Algorithm
• Every Processor knows its own index (usually
indicated by variable i)
• Vector Sum

y Write x into Mi
5
Binary Fan-In
Read Mi into Largest Write Mi into
Min Delta 1 For k 1 to élg nù Read
MiDelta into x Largest
Maximum(x,Largest) Write Largest into Mi
Delta Delta 2 End For
6
Read Mi into Total Write 0 into Min Delta
1 For k 1 to élg nù Read MiDelta
into x Total x Total Write Total
into Mi Delta Delta 2 End For
7
Pointer Jumping
Read Mi Into Total For k 1 to élg nù
Read Nexti into Ptr If Ptr ¹ 0 Then
Read MPtr Into x Total Total x
NextPtr Into NewPtr Write NewPtr into
Nexti End If End For
8
Initialization of Nexti
If i n Then Write 0 Into Nexti Else
Write i1 Into Nexti End If
9
Calculate Node Depth I
If there is a Left Child
1
-1
To 1 of Left Child
0
From -1 of Left Child
10
Calculate Node Depth 2
If there is no left child
1
-1
0
11
Calculate Node Depth 3
If there is a Right Child
1
-1
From -1 of Right Child
0
To 1 of Right Child
12
Calculate Node Depth 4
If there is no right child
1
-1
0
13
• EREW - Exclusive Read, Exclusive Write
• CREW - Common Read, Exclusive Write
• CRCW - Common Read, Common Write
• All common writes must write the same thing
• Highest Priority Processor wins contest
• CREW is more powerful than EREW
• CRCW is more powerful than CREW

14
Finding Max
• Square Array of Processors Indexed by i,j

into y If x lt y Then Write False Into
Ri Else If y lt x Then Write False Into
Rj End If
15
CRCW V.S. CREW
• CRCW Max runs in constant time
• CREW Max runs in lg n time
• CRCW cannot be any better than lg p faster than
EREW

16
EREW V.S. CREW
• Finding Roots by Shortcutting Pointers
• CREW Runs in lg lg n Time
• EREW Runs in lg n Time

17
Optimal Parallel Algorithms
• NC -- The class of algorithms that run in
Q(logmn) time using Q(nk) processors
• General Boolean Functions Cannot be Computed any
Faster than Q(lg n)
• Q(lg n) is optimal for computing the sum of n
integers