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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]
For a sequence of m addition, union, or find operations on a disjoint-set forest with n nodes, the total time required is O(mα(n)), where α(n) is the extremely slow-growing inverse Ackermann function. Although disjoint-set forests do not guarantee this time per operation, each operation rebalances the structure (via tree compression) so that ...
Inverse Ackermann function. Add languages. Add links. Article; ... Download QR code; Print/export Download as PDF; Printable version; In other projects
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 ...
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations N as the result of input size n for each function. In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm.
In other words, the Ackermann hierarchy and the Goodstein hierarchy (if calling things by authors is what you care about) are completely distinct families of binary operations, even though they are both defined by (,,) = (,, (,,)), the initial conditions make them different.
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Download as PDF; Printable version; ... Example. Compute (,) ... and so does not form a hyperoperation hierarchy. n Operation Comment 0