Can the asymptotic expression $mathcal{O(log(n) cdot log(m))}$ be simplified?











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I constructed an algorithm $A$ with input $(n,m)$ and I found that it has runtime
$mathcal{O(log(n) cdot log(m))}$. I was asking myself if this expression can be simplified somehow, but I could not find a way. Do you see a possiblity here?










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    What could be simpler? You use the two input values $n,m$ once each, you apply a simple standard function to each, you combine the two by the simple operation of multiplication
    – Hagen von Eitzen
    Nov 17 at 11:21















up vote
1
down vote

favorite












I constructed an algorithm $A$ with input $(n,m)$ and I found that it has runtime
$mathcal{O(log(n) cdot log(m))}$. I was asking myself if this expression can be simplified somehow, but I could not find a way. Do you see a possiblity here?










share|cite|improve this question


















  • 1




    What could be simpler? You use the two input values $n,m$ once each, you apply a simple standard function to each, you combine the two by the simple operation of multiplication
    – Hagen von Eitzen
    Nov 17 at 11:21













up vote
1
down vote

favorite









up vote
1
down vote

favorite











I constructed an algorithm $A$ with input $(n,m)$ and I found that it has runtime
$mathcal{O(log(n) cdot log(m))}$. I was asking myself if this expression can be simplified somehow, but I could not find a way. Do you see a possiblity here?










share|cite|improve this question













I constructed an algorithm $A$ with input $(n,m)$ and I found that it has runtime
$mathcal{O(log(n) cdot log(m))}$. I was asking myself if this expression can be simplified somehow, but I could not find a way. Do you see a possiblity here?







asymptotics






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asked Nov 17 at 11:20









3nondatur

362111




362111








  • 1




    What could be simpler? You use the two input values $n,m$ once each, you apply a simple standard function to each, you combine the two by the simple operation of multiplication
    – Hagen von Eitzen
    Nov 17 at 11:21














  • 1




    What could be simpler? You use the two input values $n,m$ once each, you apply a simple standard function to each, you combine the two by the simple operation of multiplication
    – Hagen von Eitzen
    Nov 17 at 11:21








1




1




What could be simpler? You use the two input values $n,m$ once each, you apply a simple standard function to each, you combine the two by the simple operation of multiplication
– Hagen von Eitzen
Nov 17 at 11:21




What could be simpler? You use the two input values $n,m$ once each, you apply a simple standard function to each, you combine the two by the simple operation of multiplication
– Hagen von Eitzen
Nov 17 at 11:21










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The only thing I can think of is
$$mathcal O(log(n^{log m})) $$
But this is silly and not really any simpler. Go with what you have.






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    up vote
    1
    down vote



    accepted










    The only thing I can think of is
    $$mathcal O(log(n^{log m})) $$
    But this is silly and not really any simpler. Go with what you have.






    share|cite|improve this answer

























      up vote
      1
      down vote



      accepted










      The only thing I can think of is
      $$mathcal O(log(n^{log m})) $$
      But this is silly and not really any simpler. Go with what you have.






      share|cite|improve this answer























        up vote
        1
        down vote



        accepted







        up vote
        1
        down vote



        accepted






        The only thing I can think of is
        $$mathcal O(log(n^{log m})) $$
        But this is silly and not really any simpler. Go with what you have.






        share|cite|improve this answer












        The only thing I can think of is
        $$mathcal O(log(n^{log m})) $$
        But this is silly and not really any simpler. Go with what you have.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 17 at 11:23









        Matt Samuel

        36.2k63463




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