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Questions tagged [landau-notation]

Questions about asymptotic notations such as Big-O, Omega, etc.

271 questions
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What does tilde mean, in big-O notation?

I'm reading a paper, and it says in its time complexity description that time complexity is $\tilde{O}(2^{2n})$. I have searched the internet and wikipedia, but I can't find what this tilde signifies in big-O/Landau notation. In the paper itself I…
Johannes Schaub - litb
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Are $\log_{10}(x)$ and $\log_2(x)$ in the same big-O class of functions?

Are $\log_{10}(x)$ and $\log_{2}(x)$ in the same big-O class of functions? In other words, can one say that $\log_{10}(x)=O(\log x)$ and $\log_{2}(x)=O(\log x)$?
David Faux
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Is $\{\Theta(f)|f:\mathbb{N}\rightarrow\mathbb{N}\}$ Dedekind-complete?

Let $\Theta$ and $o$ be defined as usual (Landau-notation). For two equivalence classes defined by $\Theta$ we define $$\Theta(f) <_o \Theta(g) :\Leftrightarrow f \in o(g)\qquad.$$ Let $$\mathbb{F}:= \{\Theta(f)\mid…
frafl
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Finding the constants in Landau notation

I am trying to find the constants $n_0$ and $c$ to show that some given functions belong to the $O(\cdot)$ equivalence class. But, while it seems easy, I am not sure whether I am allowed to do what I will showcase below, or rather, what decides…
imbAF
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Order Notation - Why can't $c$ be in terms of $n$?

For $f(n)$ to be in $O(g(n))$, there must exist a $c > 0$ and $n_0 > 0$ such that $$0 \leq f(n) \leq cg(n) \text{ for all }n \geq n_0\,.$$ I found a solution to a question where my $c$ is in terms of $n$, but my friend says you can't have that. I'd…
Chara
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Is $O(N+M)$ exponential or polynomial?

So In a review section, our professor asked: Given integers $N$ and $M$ Is $O(N+M)$ exponential or polynomial. It's exponential, but I just don't see how that is. I would have thought it's linear.
Daver Muzaffar
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Big O notation question for set insertion with sequential scan?

A friend and I are asking some questions on Big O Notation. We have an operation that requires a sequential scan on insertion of an element O(n). The insertion itself of an element is O(1). We are inserting a whole set of n items. We both agree…
Evan Carroll
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Is this a correct way to thing about asymptotic notations?

I am reading a book on algorithms. It says that $2n^2+3n+1=2n+\Theta(n)$. For a person like me who has studied some set theory but not from axioms, this notation seems a bit insane. I was wondering why are we allowed to compute a sum of a polynomial…
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