Time Complexity
| Minimum edge weight data structure | Time complexity (total) |
|---|---|
| adjacency matrix, searching | O(V2) |
| binary heap and adjacency list | O((V + E) log V) = O(E log V) |
| Fibonacci heap and adjacency list | O(E + V log V) |
A simple implementation using an adjacency matrix graph representation and searching an array of weights to find the minimum weight edge to add requires O(V2) running time. Using a simple binary heap data structure and an adjacency list representation, Prim's algorithm can be shown to run in time O(E log V) where E is the number of edges and V is the number of vertices. Using a more sophisticated Fibonacci heap, this can be brought down to O(E + V log V), which is asymptotically faster when the graph is dense enough that E is ω(V).
Read more about this topic: Prim's Algorithm
Famous quotes containing the words time and/or complexity:
“Unquiet wanderer
Draw the Glasnevin coverlet anew
About your head till the dust stops your ear,
The time for you to taste of that salt breath
And listen at the corners has not come;
You had enough of sorrow before death—”
—William Butler Yeats (1865–1939)
“The price we pay for the complexity of life is too high. When you think of all the effort you have to put in—telephonic, technological and relational—to alter even the slightest bit of behaviour in this strange world we call social life, you are left pining for the straightforwardness of primitive peoples and their physical work.”
—Jean Baudrillard (b. 1929)