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how to find shortest cycle in weighted undirected graph?
By Halym2007, history, 13 months ago, In English

can you share your idea?

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13 months ago, # |
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Dijkstra Algorithm for Each Vertex

Run Dijkstra from each vertex. While doing so, keep track of the shortest path to each other vertex.

When considering a new edge during the algorithm, if the edge leads to a vertex already visited, you have found a cycle. Calculate its length and compare it with the shortest cycle found so far.

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    13 months ago, # ^ |
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    what is your time complexity?

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      13 months ago, # ^ |
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      $$$O(EV\log V)$$$

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        13 months ago, # ^ |
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        Is there any way to find with MST(minimum spanning tree)?

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          13 months ago, # ^ |
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          Are you looking for something faster than $$$O(EV)$$$? If yes, that isn't possible with MST. Consider a graph where every edge has the same weight. Now the MST is just any spanning tree and it doesn't give you any extra info. This case can be solved in $$$O(EV)$$$ by replacing dijkstra with bfs since all edges have the same weight, but nothing faster is possible afaik.

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    13 months ago, # ^ |
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    You can also do this in O(V^3) using Floyd

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