Lecture 4

Notes below are meant to supplement the scribed notes.

Improved MST Algorithm (Section 4.4)

Compared to the priority queue, the Fibonacci heap has a better amortized time for the insert and decrease-key operations, which is \(O(1)\) instead of \(O(\log V)\). Recall that in Prim's algorithm, we need to perform \(O(E)\) decrease-key operations and \(O(V)\) insert operations. Therefore, by using Fibonacci heaps, the overall time complexity of Prim's algorithm can be improved to \(O(E + V \log V)\).