What is the time complexity of Dijkstra's algorithm with a Fibonacci heap?

Conditions

• The implementation uses a Fibonacci heap data structure for the priority queue.
• $|V|$ represents the number of vertices.
• $|E|$ represents the number of edges.

Reasoning, step by step

1. Identify the data structure used for the priority queue (Fibonacci heap).
2. Recall the cost of extracting the minimum element and decreasing keys in a Fibonacci heap.
3. Combine these costs with the number of vertices and edges to derive the total complexity.
4. State the final Big O notation.

Example

The video explicitly states: 'The time complexity of Dijkstra's algorithm is O(|E| + |V|log|V|) when using a Fibonacci heap.' The formula is written on screen.

Common misconceptions

• Assuming this complexity applies to all implementations; using a binary heap yields $O((|E| + |V|)\log|V|)$.
• Confusing $|V|$ and $|E|$ in the formula; the log term applies to the number of vertices.

Watch the explanation

Explore next

• What is the pseudocode for Dijkstra's algorithm?
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• Why is a Fibonacci heap more efficient than a binary heap for this algorithm?