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 • 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 • 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 • 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

9. 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.

10. 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

11. 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) ]

12. Routing Mechanisms • Algorithm Based Routing: • Source Routing • Table of Source (00) from last slide

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