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The inverse of the Ackermann function appears in some time complexity results. For instance, the disjoint-set data structure takes amortized time per operation proportional to the inverse Ackermann function, [24] and cannot be made faster within the cell-probe model of computational complexity. [25]
Here, the function () is the inverse Ackermann function. The inverse Ackermann function grows extraordinarily slowly, so this factor is 4 or less for any n that can actually be written in the physical universe. This makes disjoint-set operations practically amortized constant time.
In graph theory a minimum spanning tree (MST) of a graph = (,) ... is the inverse Ackermann function. Thus the total runtime of the algorithm is in ...
The final iteration through all edges performs two find operations and possibly one union operation per edge. These operations take amortized time O(α(V)) time per operation, giving worst-case total time O(E α(V)) for this loop, where α is the extremely slowly growing inverse Ackermann function. This part of the time bound is much smaller ...
The complexity for finding a minimum tree spanner in a digraph is ((+) (+,)), where (+,) is a functional inverse of the Ackermann function The minimum 1-spanner of a weighted graph can be found in O ( m n + n 2 log ( n ) ) {\displaystyle {\mathcal {O}}(mn+n^{2}\log(n))} time.
In computing and graph theory, ... , where n is the number of vertices and α is the inverse Ackermann function. [1] [2] Decremental connectivity ...
In three dimensions, unit distance graphs of points have at most / edges, where is a very slowly growing function related to the inverse Ackermann function. [28] This result leads to a similar bound on the number of edges of three-dimensional relative neighborhood graphs . [ 29 ]
The best bounds known on λ s involve the inverse Ackermann function. α(n) = min { m | A(m,m) ≥ n}, where A is the Ackermann function. Due to the very rapid growth of the Ackermann function, its inverse α grows very slowly, and is at most four for problems of any practical size. [3] Using big O and big Θ notation, the following bounds are ...