Basic communication operations on a mesh

1
Basic communication operations on a mesh

• One-to-all broadcast
• All-to-all broadcast
• All-to-all personalized communication
• Based on the ring (linear array) communication
  algorithm

2
Mesh one-to-all broadcast

• Phase 1 a row of the mesh with the sender
  performs a one-to-all broadcast on ring(linear
  array)
• Phase 2 each column of the mesh performs a
  one-to-all broadcast on ring(linear array)

3
Phase 1 A row of the mesh with the sender 0
performs a one-to-all broadcast on the linear
array
2
3
(0)
0
1
The sender
One-to-all broadcast
4
After phase 1
2
3
(0)
(0)
0
1
5
Phase 2 Each column of the mesh performs a
one-to-all broadcast on the linear array
2
3
(0)
(0)
0
1
6
After phase 2
(0)
(0)
2
3
(0)
(0)
0
1
7

• Phase 1 takes time
• Phase 2 takes time
• The total time

8
All-to-all broadcast
2
3
(2)
(3)
message
0
1
(1)
(0)
9
Phase 1 Each row of the mesh performs an
all-to-all broadcast on the linear array
(2)
(3)
2
3
(0)
(1)
0
1
10
After phase 1
(2,3)
2
3
(2,3)
(0,1)
0
1
(0,1)
11

• Phase 1 takes time
• After phase 1,
• the size of each message

12
Phase 2 Each column of the mesh performs an
all-to-all broadcast on the linear array
2
3
(2,3)
(2,3)
1
0
(0,1)
(0,1)
13
After phase 2
2
3
(0,1, 2,3)
(0,1, 2,3)
1
0
(0,1, 2,3)
(0,1, 2,3)
14

• Phase 1 takes time
• After phase1, the message size
• Phase 2 takes time

15
All-to-all personalized communication

• Initially, every node has p messages.
• Each node assembles its data into groups

16
3(0),3(2) 3(1),3(3)
2(0),2(2) 2(1),2(3)
2
3
0(0),0(2) 0(1),0(3)
1(0),1(2) 1(1),1(3)
0
1
17
Phase 1 Each row of the mesh performs an
all-to-all personalized communication on the
linear array
3(0),3(2) 3(1),3(3)
2(0),2(2) 2(1),2(3)
2
3
0(0),0(2) 0(1),0(3)
1(0),1(2) 1(1),1(3)
0
1
18
After phase 1
2(1),2(3) 3(1),3(3)
2(0),2(2) 3(0),3(2)
2
3
0(0),0(2) 1(0),1(2)
0(1),0(3) 1(1),1(3)
0
1
19
Phase 2
2(1),2(3) 3(1),3(3)
2(0),2(2) 3(0),3(2)
2
3
0(0),0(2) 1(0),1(2)
0(1),0(3) 1(1),1(3)
0
1
20
Each column of the mesh performs an all-to-all
Personalized communication on the linear array
2(1),2(3) 3(1),3(3)
2(0),2(2) 3(0),3(2)
2
3
0(0),0(2) 1(0),1(2)
0(1),0(3) 1(1),1(3)
0
1
21
After phase 2
0(3),2(3) 1(3),3(3)
0(2),2(2) 1(2),3(2)
2
3
0(0),2(0) 1(0),3(0)
0(1),2(1) 1(1),3(1)
0
1
22

• In phase 1
• The number of processors
• The message size on each processor
• The time for phase 1

The time on a ring
23

• In phase 1
• The number of processors
• The message size on each processor
• The time for phase 1
• the time for phase 2 the time for phase 1
• The total time

24
Communication times on a mesh

• One-to-all broadcast / all-to-one reduction
• All-to-all broadcast / all-to-all reduction
• All-to-all personalized communication