1 Routing Algorithms. 2 Outline zBellaman-Ford Algorithm zDijkstra Algorithm.

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Presentation transcript:

1 Routing Algorithms

2 Outline zBellaman-Ford Algorithm zDijkstra Algorithm

3 Bellman-Ford Algorithm(1/3) Source Node Shortest paths problem arcs lengths as indicated Definition is the shortest (≤h) path length from node 1 to node i Bellman-Ford Algorithm Initially, For each successive h≥0, Example I

4 Bellman-Ford Algorithm(2/3) Shortest paths using at most 2 arcs Shortest paths using at most 1 arcs

5 Bellman-Ford Algorithm(3/3) Final tree of shortest paths Shortest paths using at most 3 arcs

6 Dijkstra’s Algorithm(1/3) Initially P={1}, D 1 =0, and Step1. (Find the closest node). Find such that Set. If P contains all nodes then stop ; the algorithm is complete Step2. (Updating of labels). For all set Go to Step1.

7 Dijkstra’s Algorithm(2/3) zExample of Dijkstra’s Algorithm

8 Dijkstra’s Algorithm(3/3) P = {1,2} P = {1,2,5} P = {1,2,3,4,5}