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CS223-0325-Dijkstra

# CS223-0325-Dijkstra - 7 Dijkstra’s Algorithm Dijkstra’s...

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CS223 Advanced Data Structures and Algorithms 1 Dijkstra’s Shortest Path Algorithm Dijkstra’s Shortest Path Algorithm Neil Tang Neil Tang 03/25/2008 03/25/2008

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CS223 Advanced Data Structures and Algorithms 2 Class Overview Class Overview The shortest path problem Applications Dijkstra’s algorithm Implementation and time complexities
CS223 Advanced Data Structures and Algorithms 3 Shortest Path Problem 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.

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CS223 Advanced Data Structures and Algorithms 4 An Example An Example
CS223 Advanced Data Structures and Algorithms 5 Another Example Another Example

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

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Unformatted text preview: 7 Dijkstra’s Algorithm Dijkstra’s Algorithm CS223 Advanced Data Structures and Algorithms 8 Dijkstra’s Algorithm Dijkstra’s Algorithm CS223 Advanced Data Structures and Algorithms 9 Dijkstra’s Algorithm Dijkstra’s Algorithm CS223 Advanced Data Structures and Algorithms 10 Dijkstra’s Algorithm Dijkstra’s Algorithm CS223 Advanced Data Structures and Algorithms 11 Dijkstra’s Algorithm Dijkstra’s Algorithm CS223 Advanced Data Structures and Algorithms 12 Dijkstra’s Algorithm Dijkstra’s Algorithm CS223 Advanced Data Structures and Algorithms 13 Dijkstra’s Algorithm Dijkstra’s Algorithm CS223 Advanced Data Structures and Algorithms 14 Implementation and Time Complexities 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|)...
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