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Dijkstra’s Shortest Path Algorithm Neil Tang 03/25/2008

Dijkstra’s Shortest Path Algorithm Neil Tang 03/25/2008. Class Overview. The shortest path problem Applications Dijkstra’s algorithm Implementation and time complexities. Shortest Path Problem. Weighted path length (cost): The sum of the weights of all links on the path.

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Dijkstra’s Shortest Path Algorithm Neil Tang 03/25/2008

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  1. Dijkstra’s Shortest Path Algorithm Neil Tang03/25/2008 CS223 Advanced Data Structures and Algorithms

  2. Class Overview • The shortest path problem • Applications • Dijkstra’s algorithm • Implementation and time complexities CS223 Advanced Data Structures and Algorithms

  3. Shortest Path Problem • Weighted path length (cost): The sum of the weights of all links on the path. • The single-source shortest path problem: Given a weighted graph G and a source vertex s, find the shortest (minimum cost) path from s to every other vertex in G. CS223 Advanced Data Structures and Algorithms

  4. An Example CS223 Advanced Data Structures and Algorithms

  5. Another Example CS223 Advanced Data Structures and Algorithms

  6. Applications • Digital map • Computer network • Travel planning CS223 Advanced Data Structures and Algorithms

  7. Dijkstra’s Algorithm CS223 Advanced Data Structures and Algorithms

  8. Dijkstra’s Algorithm CS223 Advanced Data Structures and Algorithms

  9. Dijkstra’s Algorithm CS223 Advanced Data Structures and Algorithms

  10. Dijkstra’s Algorithm CS223 Advanced Data Structures and Algorithms

  11. Dijkstra’s Algorithm CS223 Advanced Data Structures and Algorithms

  12. Dijkstra’s Algorithm CS223 Advanced Data Structures and Algorithms

  13. Dijkstra’s Algorithm CS223 Advanced Data Structures and Algorithms

  14. Implementation and Time Complexities • Trivial: O(|V|2 + |E|) = O(|V|2) • Heap: deleteMin |V| times + decreaseKey |E| times O(|V|log|V| + |E|log|V|) = O (|E|log|V|) • Fibonacci heap: O(|E| + |V|log|V|) CS223 Advanced Data Structures and Algorithms

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