Show that the method is equivalent to dijkstra''s algorithm

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Reference no: EM131121980

Relation of Primal-Dual and Dijkstra) Consider the shortest path problem with node 1 being the origin and all other nodes being destinations. Formulate this problem as a minimum cost flow problem with the origin having supply N - 1 and all destinations having demand 1. Assume that all arc lengths are nonnegative. Start with all flows and prices equal to zero, and apply the primal-dual method. Show that the method is equivalent to Dijkstra's algorithm. In particular, each augmentation uses a shortest path from the origin to some destination, the augmentations are done in the order of the destinations' proximity to the origin, and upon termination, p1 -pi gives the shortest distance from 1 to each destination i that can be reached from the origin via a forward path.\

Reference no: EM131121980

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