Interconnection Networks

Lecture 9 : Valentines Day SpecialRouting Algorithms and Mechanism

Prof. Chung-Kuan Cheng University of California San Diego Transcribed by: Jason Thurkettle

Topics Routing

Algorithms Deterministic Oblivious Adaptive

Mechanisms

Traffic Patterns Neighbor -> dx = sx

+ 1 mod k Transpose: di = si

+ b/2 mod b Complement

Tornado

S0 S1 S2 S3

S0 S1 S2 S3

B = 4

ksd kxx mod)11( 2

ii sd

Deterministic Routing Algorithm Deterministic Routing Algorithm

Ex: Butterfly Route according to address of the

destination K-ary N-cube network

Route in a shortest path The order of the dimension is set

Deterministic Routing

1 2 3 4 5 6

All links bidirectional

Only uses half of the available resources

S0 S1 S2 S3

S0 S1 S2 S3

B = 4

Oblivious Routing Algorithm Oblivious Routing Algorithm

Variant’s Algorithm K-ary N-cube

Send each packet on average distance of K/4 in each of N dimensions

Route the packet to the destination Minimal Oblivious Routing: on Tourous

Find minimal quadrant between sender (S) and destination (D) (S&D)

Select an intermediate node X in the quadrant Route S to X and X to D (where X is chosen

randomly)

Oblivious Routing Algorithm Oblivious Routing Algorithm

Load Balanced Routing: Find quadrant: in each dimension I

Select the short direction Di = Di with p=(K-Δi)/K Select the long direction Di = Di with p=Δi/K

Repeat second step of Minimal Oblivious Routing Repeat third step of Minimal Oblivious Routing

Oblivious Routing Algorithm Traffic Models vs Bandwidth Usage

δ-array 2-cube E-cube Valiant Minimal Load-Balanced

Nearest neighbor 4 .5 4 2.33

Uniform 1 .5 1 .76

Bit-Compliment .5 .5 .4 .42

Transpose .25 .5 .54 .57

Tornado .33 .5 .33 .53

Worst Case .25 .5 .21 .31

Adaptive Routing Algorithm Adaptive Routing Algorithm

Productive hop The packet goes closer to its destination

Local Congestion Length of Queue

Minimal Adaptive Routing The router chooses only productive hops If these are choices, the hop with minimal

congestion is chosen.

Adaptive Routing Algorithm Adaptive Routing Algorithm

Fully Adaptive Routing The router chooses a productive hop if the

congestion is less than a threshold. Otherwise the hop with minimal congestion is taken (with a probability)

Live lock is possible Load Balanced Adaptive Routing

We use load balanced oblivious routing to choose the quadrant

The minimum adaptive routing is performed in the quadrant

Routing Mechanisms Table Based Routing

R : NxN -> P(p) N: Node Deterministic – determined at source

R : NxN -> P(c) C: Channel R : NxN -> P(c) P: Path

Algorithm Based Routing: Source Routing [R : SxD -> P(s) ]

Routing Mechanisms Algorithm Based Routing:

Source Routing Table of Source (00) from last slide

Dest Route 0 Route 1

00 X X

01 Ex WWWx

02 EEx WWx

03 Wx EEEx

10 Nx Sx

11 NEx ENx

12 NEEx WWNx

13 NWx WNx

Routing Mechanisms Algorithm Based Routing:

Source Routing The path is chosen at the source node. Each source node contains a table of the route per

destination. The advantage: simplified the packet movement between

source and destination. Node – Table Routing

Each node has a table with index=destination, entry=next hop

The method can be used for adaptive routing

0 0 X X X

0 1 0 X X

0 1 1 0 X

0 1 1 1 1