Kruskal is O(E log E); your derivation is right. You could also say O(E log V) because E <= V * V, so log(E) <= 2 log(V) (I don’t know why I remember that, other than that I think a prof put that on an exam at one point…)
Yes, it does. One method for computing the maximum weight spanning tree of a network G – due to Kruskal – can be summarized as follows. Sort the edges of G into decreasing order by weight. Let T be the set of edges comprising the maximum weight spanning tree. Set T = ∅. Add the … Read more
Use Prim’s algorithm when you have a graph with lots of edges. For a graph with V vertices E edges, Kruskal’s algorithm runs in O(E log V) time and Prim’s algorithm can run in O(E + V log V) amortized time, if you use a Fibonacci Heap. Prim’s algorithm is significantly faster in the limit … Read more