Dijkstra's algorithm runs in time O(n lg n + m) with a Fibonacci heap, which is at least as efficient as using either an unsorted array or a min-heap.
For each weighted, directed graph with positive weights, Dijkstra's algorithm finds the shortest path. It can handle cycles-based graphs, although negative weights will result in inaccurate results for this approach. We therefore assume that w(e) 0 for all e > E in this case.
Dijkstra's algorithm is depicted by the pseudocode in Algorithm 4.12. In order to retain the unprocessed vertices with their shortest-path estimates est(v) as key values, the method maintains a priority queue minQ. The vertex u with the lowest est(u) is then repeatedly extracted from minQ, and all edges occurring from u to any vertex in minQ are relaxed. The method will consider one vertex as processed once it has been extracted from minQ and all relaxations via it have been finished.
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