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I have been working in the time analysis for an algorithm and finally I got a curve that fits:

$O(2^{(\log_2(N)^{2.01})})$

N is the number of elements.

I'm right to say the above time complexity is quasi-polynomial?

Raphael
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Jesus Salas
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  • What "elements"? That is crucial here. (Also, don't use "time complexity"; you have an asymptotic upper bound.) – Raphael Dec 03 '14 at 11:29
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    Oh, I just saw this: "I got a curve that fits" -- oh no, don't do that! What you are doing is not analysis but fortune-telling. If you want to learn about "real" algorithm analysis, you may want to head over to our reference questions on the matter. – Raphael Dec 03 '14 at 16:04
  • @Raphael log2 = log (base 2) (i.e. Log2(32) = 5 ), N = input size (number of input elements). – Jesus Salas Dec 03 '14 at 17:57
  • @Raphael I was focusing to double check the resultant time complexity. There is no curve that fits" the result is an asymptotic worst case analysis for an algorithm – Jesus Salas Dec 03 '14 at 17:59
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    "input size" and "number of input elements" is not necessarily the same. Which size does each element have? Are they numbers? – Raphael Dec 03 '14 at 18:00
  • Yes, they are numbers and Input Length and Size of each element are equal (N=P) being N the number of input elements and P the number of bits required to represent each input element, so for instance:

    SET= {1,22,333,4444,55555,666666,7777777,10170128,10596586,10833720,11300828,12152672,16453700,18839720,19496780,22409892,2,493424,26606324,26985764,30017152,30169256,30345762,30371136,30561184,31495936}

    N = 25 and P = 25, Log2(Max(Set)) = 25, or maybe I can use LOG2(SUM(SET)) = 29.

     – Jesus Salas Dec 03 '14 at 18:10

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Quasi-polynomial means different things to different people, but in many contexts it means a running time of the form $O(2^{O(\log^{O(1)} N)})$, to which your example conforms.

Yuval Filmus
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