1. Algebra and algorithms for QoS path computation and hop-by-hop routing in the internet

2. Outline Introduction and Contribution An algebra for QoS path problems QoS path computation QoS Hop-by-hop routing QoS Multirouting

3. Introduction Shortest path routing: Dijkstra’s Algorithm Hop-by-hop routing: local, depending on destination only For QoS, both have limitations Contribution 1) Revise Dijkstra’s algorithm 2) Eliminate loop in hop-by-hop routing

4. An algebra for QoS path problems

5. Notations

7. QoS path computation Lexicographic-lightest path

9. S-lightest path

10. A generalized Dijkstra’s Algorithm

14. QoS Hop-by-hop routing Nonoptimality When Isotonicity Fails