Why is the Ackerman function related to the amortized complexity of the join-search algorithm used for disjoint sets?

Can someone give me an intuitive explanation of why the Ackermann http://en.wikipedia.org/wiki/Ackermann_function function is related to the amortized complexity of the join-search algorithm used for the disjoint sets http://en.wikipedia.org/wiki / Disjoint-set_data_structure ?

The analysis in the structure of the Tarjan data structure is not very intuitive.

I also reviewed it in Introduction to Algorithms, but it also seems too rigorous and unintuitive.

Thank you for your help!

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Applies to non-mated forests

from Wikipedia

(on searching and combining) These two methods complement each other; applied together, the amortized time per operation is only O (ฮฑ (n)), where ฮฑ (n) is the inverse of the function f (n) = A (n, n), and A is the extremely fast-growing Ackerman function. Since ฮฑ (n) is the inverse of this function, ฮฑ (n) is less than 5 for all remotely practical values โ€‹โ€‹of n. Thus, the amortized operating time for the constant works efficiently.

So why Ackerman?

from Kruskal algoritm

Lg * n function

, lg * n - , , lg n. , lg lg n, lg n. f (n) = 2 ^ 2 ^ 2 ^... ^ 2, . n >= 5 f (n) . , , f (n) n, . , O (e). , , , O (e) . , , lg * n A (p, n) A - , a . lg * n, , .

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