Color-based task mapping for Dragonfly systemscourses.knox.edu/cs399/notes/coloringBased.pdf · Use 2D algorithm to color cube’s front face (coloring cubes not squares) Color each

Color-based task mapping for Dragonfly systems

By Allen Treichel and Mohammad Kamran

What is Task Mapping in Dragonfly?● Assigning job tasks to computing elements

● Goals:○ Maximize locality, and reduce number of network hops as a way to reduce bandwidth

consumption

What’s wrong with traditional Task mapping?A. Nothing!B. Traffic concentrated on only a few global linksC. Maximizes localityD. Causes bottleneckE. None of the above (one or more)

What’s wrong with traditional Task mapping?A. Nothing!B. Traffic concentrated on only a few global linksC. Maximizes localityD. Causes bottleneckE. Not exactly one of the above

What is Color-Based Task Mapping-Also known as “Balanced Adjacency Coloring”

-Done via the assignment of colors to cells of a matrix

Goals:

-The number of times each color is used should be equal or within one of each other

-The number of times each pair of colors is adjacent should be equal or within one of each other

What is Color-Based Task Mapping-There are no requirements on the number of times a color is adjacent to itself

Example of a 6 x 6 balanced adjacency coloring with 6 colors (n):

1 2 3 4 5 6

3 1 5 2 6 4

2 4 1 6 3 5

5 3 6 1 4 2

4 6 2 5 1 3

6 5 4 3 2 1

Paper Goals● Demonstrate how traditional task mapping is counterproductive since it

creates hot spots

● Introduce balanced adjacency coloring (BAC) that can evenly spread network traffic in order to reduce hot spots

n x n with n colors● Every grid cell is on exactly one line

● Each color appears exactly n times

● Each color pair is adjacent four times

1 2 3 4 5 6

3 1 5 2 6 4

2 4 1 6 3 5

5 3 6 1 4 2

4 6 2 5 1 3

6 5 4 3 2 1

3D Algorithm ● Use 2D algorithm to color cube’s front face (coloring cubes not squares)

● Color each horizontal part of the cube using 2D algorithm

● Each color used an equal amount of times

● Each slice has an equal number of adjacencies between each pair

Which of the following is true about a balanced adjacency coloring for an n x n grid using 2n colors?

A. Each color appears exactly n/2 timesB. When n is even, each color is non-adjacent to one color exactly onceC. Each color is adjacent to all others exactly onceD. When n is odd, some pairs have multiple adjacenciesE. Not exactly one of the above

Which of the following is true about a balanced adjacency coloring for an n x n grid using 2n colors?

A. Each color appears exactly n/2 timesB. When n is even, each color is non-adjacent to one color exactly onceC. Each color is adjacent to all others exactly onceD. When n is odd, some pairs have multiple adjacenciesE. Not exactly one of the above (B and D)

n x n with 2n colors-Uses 2 reference rows instead of one

-Lines are formed the same as in n x n with n colors, except now each is associated with 2 colors which alternate down the line

-When n is even each color appears n/2 times, each color is non-adjacent to one color and adjacent to all others exactly once

-When n is odd half the colors appear ⌊n/2⌋, half appear ⌈n/2⌉

-Only balanced when n is even

Example of a 6 x 6 coloring with 12 colors (2n):

1 2 3 4 5 6

7 8 9 10 11 12

2 4 1 6 3 5

9 7 11 8 12 10

4 6 2 5 1 3

11 9 12 7 10 8

Why does B-BAC Perform better than P-BAC A. It uses 2n coloring algorithmB. It uses less global linksC. Better utilizes local linksD. What’s B-BAC and P-BAC?E. Not exactly one of the above

Why does B-BAC Perform better than P-BAC A. It uses 2n coloring algorithmB. It uses less global linksC. Better utilizes local linksD. What’s B-BAC and P-BAC?E. Not exactly one of the above

P-BAC Mapping● Uses n x n algorithm

● Cells are arbitrarily assigned to the group nodes

● Global links used in all shortest paths

● Ignores local links which causes congestion in global links

B-BAC Mapping-Compromise between blocking and and coloring-based strategy

-Uses blocking to keep some traffic within a switch/group

-Reduces amount of traffic on global links by ~half while keeping global link traffic mostly balanced

-Divides job into 2 x 2 subgrids to form a grid size of (n/2) x (n/2) of task units, each containing 4 cells of the grid

-All mesh sizes are multiples of 4, so n is always even

P-BAC vs. B-BAC with Minimal Routing-B-BAC superior to P-BAC

Comparing Blocking-based with B-BAC