When should I use Kruskal as opposed to Prim (and vice versa)?

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 differenc

Answer 1

If we stop the algorithm in middle prim's algorithm always generates connected tree, but kruskal on the other hand can give disconnected tree or forest

Answer 2

The best time for Kruskal's is O(E logV). For Prim's using fib heaps we can get O(E+V lgV). Therefore on a dense graph, Prim's is much better.

Answer 3

Kruskal time complexity worst case is O(E log E),this because we need to sort the edges. Prim time complexity worst case is O(E log V) with priority queue or even better, O(E+V log V) with Fibonacci Heap. We should use Kruskal when the graph is sparse, i.e.small number of edges,like E=O(V),when the edges are already sorted or if we can sort them in linear time. We should use Prim when the graph is dense, i.e number of edges is high ,like E=O(V²).

Answer 4

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.