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 transcript:

BIDIRECTIONAL DIJKSTRA Navid adham

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

Dijkstra

Network flow

Bidirectional

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

Bidirectional

Proof

Detail

Implementation

Sample

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