AF-heap

In computer science, the AF-heap is a type of priority queue for integer data, an extension of the fusion tree using an atomic heap proposed by M. L. Fredman and D. E. Willard.

Using an AF-heap, it is possible to perform $m$ insert or decrease-key operations and $n$ delete-min operations on machine-integer keys in time $O(m + n log n / log log n)$. This allows Dijkstra's algorithm to be performed in the same $O(m + n log n / log log n)$ time bound on graphs with $n$ edges and $m$ vertices, and leads to a linear time algorithm for minimum spanning trees, with the assumption for both problems that the edge weights of the input graph are machine integers in the transdichotomous model.