1. Dijkstra’s Shortest Path Algorithm Neil Tang 3/2/2010
CS223 Advanced Data Structures and Algorithms

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

3. CS223 Advanced Data Structures and Algorithms
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. CS223 Advanced Data Structures and Algorithms
An Example
CS223 Advanced Data Structures and Algorithms

5. CS223 Advanced Data Structures and Algorithms
Another Example
CS223 Advanced Data Structures and Algorithms

6. CS223 Advanced Data Structures and Algorithms
Applications
Digital map
Routing in a computer network
CS223 Advanced Data Structures and Algorithms

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

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

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

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

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

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

13. CS223 Advanced Data Structures and Algorithms
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