1. Interconnection Networks
Lecture 9 : Valentines Day Special
Routing Algorithms and Mechanism
Prof. Chung-Kuan Cheng
University of California San Diego
Transcribed by: Jason Thurkettle

2. Topics
Routing
Algorithms
Deterministic
Oblivious
Adaptive
Mechanisms

3. Traffic Patterns Neighbor -> dx = sx + 1 mod k
Transpose: di = si + b/2 mod b
Complement
Tornado

4. 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

5. Deterministic Routing
Only uses half of the available resources

6. 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)

7. 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

8. Oblivious Routing Algorithm
Traffic Models vs Bandwidth Usage
δ-array 2-cube
E-cube
Valiant
Minimal
Load-Balanced
Nearest neighbor 4 .5
2.33
Uniform 1
.76
Bit-Compliment .4
.42
Transpose
.25
.54
.57
Tornado
.33
.53
Worst Case
.21
.31

9. 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.

10. 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

11. Routing Mechanisms Table Based Routing Algorithm 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) ]

12. Routing Mechanisms Algorithm Based Routing: Source Routing
Table of Source (00) from last slide
Dest
Route 0
Route 1 00 X 01 Ex
WWWx 02
EEx
WWx 03 Wx
EEEx 10 Nx Sx 11
NEx
ENx 12
NEEx
WWNx 13
NWx
WNx

13. 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 X 1