1. BIDIRECTIONAL DIJKSTRA Navid adham

2. History Dijkstra: 1959 Dantzig method: 1960 “On the shortest route through a network” / management science Just an idea! Berge and Ghouila-Houri: 1962 Incorrect stopping criterion Dreyfus: 1969 Correct stopping A bug in algorithm Helgason and Kennington and Stewart Dijkstra’s two-tree shortest path algorithm

3. Dijkstra

4. Network flow

7. Bidirectional

8. Book exercises Proof: the dijkstra algorithm find shortest path to all node

9. Bidirectional

10. Proof

11. Detail

14. Implementation

16. Sample

17. Summary On 80 problems containing 2000 nodes and 2,000,000 edges. Classical Dijkstra: required a scan over approximately: 50% of the problem nodes. 7.5 seconds/problem The two-tree: only required a scan over: 6% of the problem nodes 1.7 seconds/problem