Kruskal vs Prim

Question

I was wondering when one should use Prim's algorithm and when Kruskal's to find the minimum spanning tree? They both have easy logics, same worst cases, and only difference is implementation which might involve a bit different data structures. So what is the deciding factor?

Answer 1

Kruskal can have better performance if the edges can be sorted in linear time, or are already sorted.

Prim's better if the number of edges to vertices is high.

Answer 2

I know that you did not ask for this, but if you have more processing units, you should always consider Borůvka's algorithm, because it might be easily parallelized - hence it has a performance advantage over Kruskal and Jarník-Prim algorithm.

Answer 3

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 when you've got a really dense graph with many more edges than vertices. Kruskal performs better in typical situations (sparse graphs) because it uses simpler data structures.

Answer 4

One important application of Kruskal's algorithm is in single link clustering.

Consider n vertices and you have a complete graph.To obtain a k clusters of those n points.Run Kruskal's algorithm over the first n-(k-1) edges of the sorted set of edges.You obtain k-cluster of the graph with maximum spacing.