lecture 21

CS 332: Algorithms S-S Shortest Path: Dijkstra’s Algorithm Disjoint-Set Union Amortized Analysis

Review: Single-Source Shortest Path ,[object Object],[object Object],[object Object],[object Object]

Review: Shortest Path Properties ,[object Object],[object Object],[object Object]

Review: Relaxation ,[object Object],[object Object],[object Object],[object Object],[object Object],9 5 2 7 5 2 Relax 6 5 2 6 5 2 Relax

Review: Bellman-Ford Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Initialize d[], which will converge to shortest-path value  Relaxation: Make |V|-1 passes, relaxing each edge Test for solution: have we converged yet? Ie,  negative cycle?

Review: Bellman-Ford Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],What will be the running time?

Review: Bellman-Ford ,[object Object],[object Object],[object Object],[object Object]

DAG Shortest Paths ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Dijkstra’s Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object]

Dijkstra’s Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Relaxation Step Note: this is really a call to Q->DecreaseKey() B C D A 10 4 3 2 1 5 Ex: run the algorithm

lecture 21

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lecture 21