How do I find the shortest path from every vertex vvv to vertex sss, where v,s∈Vv,s∈Vv,s \in V?
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Let G(V,E)G(V,E)G(V,E) be a directed graph with positive weights on its edges, and let s∈Vs∈Vs \in V be a node. Suggest an algorithm that in time O((|V|+|E|)log|V|)O((|V|+|E|)logâ¡|V|)O((|V| + |E|) \log |V|) time algorithm that finds, for every vertex vvv, what is the length of the shortest path vvv to sss?
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Answer:
Run http://en.wikipedia.org/wiki/Dijkstra's_algorithm in the reverse graph of GGG, where sss is the source. The edges of the shortest path from sss to a node v(v∈V)v(v∈V)v ( v \in V ) in the reverse graph, will form a shortest path from vvv to sss in the original graph.
Bidhan Roy at Quora Visit the source
Other answers
First reverse the direction of all edges, then use dijkstra algorithm. Dijkstra algorithm computes shortest path from 1 vertex to all other vertexes in the graph in O((|V| + |E|) \log |V| ) . You can then back trace all of those paths to return the answer.
Chan Le
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