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BIDIRECTIONAL DIJKSTRA Navid adham. History Dijkstra: 1959 Dantzig method: 1960 “On the shortest route through a network” / management science Just an.

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Presentation on theme: "BIDIRECTIONAL DIJKSTRA Navid adham. History Dijkstra: 1959 Dantzig method: 1960 “On the shortest route through a network” / management science Just an."— Presentation transcript:

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

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7 Bidirectional

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

9 Bidirectional

10 Proof

11 Detail

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14 Implementation

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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

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