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I have a MST already computed and now I am trying to update it by adding a new node v to the graph and incident edges to G. My though is that we would need to compute a new MST' from the new edge till the closest vertex of the existing MST and connect these 2 MSTs applying Kruskal's Algorithm. Though I am not sure if this would be the right choice and what would be the running time of this algorithm.

timrau
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Leon
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    I don't think I really understand what the algorithm you propose does, but it seems to me that in general, updating an MST shouldn't be faster than completely constructing a new one in general. Consider adding a vertex that is adjacent to every existing vertex, with edge weights lower than the current minimum. The new MST would then consist of just the edges incident to the new vertex and thus be completely disjoint from the old MST. – us2012 Oct 22 '13 at 23:53
  • I don't fully understand the algorithm you've described. Can you clarify what you mean by the two separate MSTs and how you'd use Kruskal's algorithm to join them? – templatetypedef Oct 22 '13 at 23:54
  • So i want to find how quickly can i update an already given MST of a graph G by adding a new vertex v and incident edges to G. What I wrote was just an idea. I am not sure how would i do this. – Leon Oct 22 '13 at 23:56

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