An Examination of Routing Algorithms for Parallel Computing - - PowerPoint PPT Presentation

An Examination of Routing Algorithms for Parallel Computing Environments

By James Kurtz Luis Martinez

Network Topology Types

Regular

Conforms to some

sort of “regular graph standard”, or definable shape:

Irregular Irregular Irregular

Network Topology Types

Regular

Conforms to some sort of

“regular graph standard”,

• r definable shape:

Ex: Cubes

Irregular Irregular Irregular

Network Topology Types

Regular

Conforms to some sort of

“regular graph standard”,

• r definable shape:

Ex: Torus (Ring)

Irregular Irregular Irregular

Network Topology Types

Regular

Conforms to some sort of

“regular graph standard”,

• r definable shape:

Ex: Meshes

Irregular Irregular Irregular

Network Topology Types

Regular Regular Regular

• Conforms to some

Conforms to some Conforms to some sort of “regular sort of “regular sort of “regular graph standard”, or graph standard”, or graph standard”, or definable shape: definable shape: definable shape:

Irregular

Don’t. Best example is the

Internet

Routing Algorithms for Regular and Irregular Topologies

I’m going to take a look at some algorithms designed for regular networks James will later show you some algorithms for irregular networks Yes, I had to make this slide, otherwise I’d forget to say that

Detour-NF

Described by Yoshinaga in his 2003 paper “Design and Evaluation of a Fault-

Tolerant Adaptive Router for Parallel Computers”

A fault-tolerant algorithm designed for a fault- tolerant router of their design. They don’t like faults. Did they mention fault-tolerance yet?

Detour-NF

They wanted a system which allowed them to switch their routing modes between deterministic and adaptive

They also wanted to further expand the adaptive

functionality to include both minimal and non- minimal routing

The reason to include both is that minimal routing doesn’t support fault-tolerance (take a drink!) Non-minimal routing can easily emulate minimal routing

• nce implemented

Detour-NF

Takes an already existing fully-adaptive algorithm

Adds one or more VC’s (in addition to any

it may already use) to any existing channels

Treated as non-minimal channels

Adds a function, R, which details how to

use the VC’s

Detour-NF

The original algorithm and R are combined

The combined algorithm favors paths chosen

by the original, but

Misroutes a message to one of the new VC’s if

there is an unavoidable block in the channel

Fault-tolerance! (seriously, I close my eyes, I

see that term…)

Routing in Detour-NF

If a channel is blocked for whatever reason, the algorithm forces it to take a turn in the “negative” direction

Followed by

whatever turns are necessary to leapfrog the compromised channel in question

“Positive” direction

turns as the first step in a leap frog are not allowed

Routing in Detour-NF

Unintended consequence:

If the path is

blocked by a faulty channel at its last turn, the path becomes unnecessarily long, since it cannot begin a leapfrog with a positive turn.

Solution: Allow 180

degree turns

Detour-NF Analysis

The hardware router they designed to implement this algorithm is more expensive

29% increase in FlipFlops compared to other

routers (dimension-order, Duato’s Protocol)

Other routers can be faster But the other routers compared, such as Duato’s Protocol, aren’t fault-tolerant

Odd-Even Turn Model

Ge-Ming Chiu of the IEEE Computer Society Can be both an element of a larger algorithm, or its own algorithm Used to determine what kinds of turns a message can make in its travels Avoids deadlock

Doesn’t use Virtual Channels

Odd-Even Turn Model

Most deadlock-avoiding, non-VC algorithms accomplish their goal by prohibiting certain kinds turns altogether, closely controlling them, or limiting their numbers Chiu says this results in an uneven efficiency across a regular mesh His turning model seeks to limit the limits

Specifically it prohibits only specific turns at

specific places, but otherwise, the message is free to turn however it wants

Odd-Even Turn Model

Picture a mesh network

Label the top North The left West, right

East

The Bottom South

NORTH SOUTH WEST EAST

Odd-Even Turn Model

Define a turn, NW, on node X such that the message is

Traveling in a northern

direction, turns at X, and heads in a western direction

NORTH SOUTH WEST EAST

Odd-Even Turn Model

Now number the rows and columns on the grid, starting from 0

NORTH SOUTH WEST EAST 1 2 1 2

Odd-Even Turn Model

Now the rules:

Rule 1. Any packet is not

allowed to take an EN turn at any nodes located in an even column, and it is not allowed to take an NW turn at any nodes located in an odd column.

NORTH SOUTH WEST EAST 1 2 1 2

Odd-Even Turn Model

Now the rules:

Rule 2. Any packet is not

allowed to take an ES turn at any nodes located in an even column, and it is not allowed to take an SW turn at any nodes located in an odd column

NORTH SOUTH WEST EAST 1 2 1 2

Odd-Even Turn Model

Now the rules:

What does this mean?

The tell-tale cycle of a deadlock is prevented by never letting the eastern- most side of that cycle form

NORTH SOUTH WEST EAST 1 2 1 2

Odd-Even Turn Model

Now the rules:

What does this mean?

180-degree turns however cannot be allowed.

NORTH SOUTH WEST EAST 1 2 1 2

Odd-Even Turn Model Analysis

An algorithm formed from the Odd- Even Turn Model performed well under high-traffic situations The xy algorithm performed best under most situations, but its un-evenness caused fluctuations in network performance.

Odd-Even Turn Model Analysis

Pros:

Easy scalability. It can be applied to a regular

mesh of most any large size.

Larger more expensive parallel systems

Can easily be incorporated into other dead-lock

free algorithms.

Since it’s not dependant on VC’s, it may even form

the basis of a VC-defining algorithm that may be used by another VC-based routing algorithm (such as R in Detour-NF perhaps)

Virtual Channel

Used to divide network into sub- networks This sub-network is virtual network Creates shorter path hops Avoid deadlock

No Virtual Channel Algorithms

Low port first Random Sancho’s Low virtual-channel first

Up* /Down* (Sancho’s)

Avoids network congestion Labels paths Remove path with largest counter Continues until one path remains

Virtual Channel Algorithms

Previous Algorithms High virtual-channel first High physical-channel first Low virtual-channel first Low physical-channel first

Virtual Channel Cont.

Descending Layers network (DL)

Divide into sub networks

All variations on Sancho’s algorithm Counters based on virtual channels Better at avoiding network congestion

Performance

High virtual channel first had a increase in throughput over low port first of 92% All DL routing algorithms were better than Up* /Down* routing algorithms

Test Results

Test Results Cont.

Questions?