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Questions tagged [little-o]

In algorithmic analysis, little-o notation is used to quantitatively state that one function grows strictly slower than another function.

Formally speaking, we say that f(n) = o(g(n)) if

limn → ∞ f(n) / g(n) = 0.

That is, the rate of growth of f(n) is strictly slower than the rate of growth of g(n).

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How do decide whether 5^n o, Θ, or ω of 7^n?

As a homework problem, I need to decide whether 5n is little-o, Θ, or little-ω of 7n with mathematical justification. I then need to repeat this after taking the logarithms of both sides. I am struggling to understand what I am being asked to do.…
user2345335
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Big O notation In this context

I’m reading a book and I came accorss this statement We finally define what it means for an algorithm to be non-private. blatantly Non private
Definition 1. An algorithm is blatantly non-private if an adversary can construct a database c 2 {0, 1}n…
hamza -
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Little-oh notation for two logarithmic functions?

I have the following function (with the natural log and log base 2): and I am trying to prove the validity of this statement. I believe it is true. All logarithms are asymptotically equivalent to each other. I am trying to write the formal proof…
greendaysbomb
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When to use Big O instead of theta or little o

A question about asymptotic notation. I've seen a lot of explanations of asymptotic notation say: θ(...) is analogous to = O(...) is analogous to <= o(...) is analogous to < Which would seem to imply that if f(n) = O(g(n)), then either f(n) =…
A Nortonsmith
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Algorithms - Both Little o and Big Omega on the same functions?

I have two functions, f(n),g(n) such that f(n)=o(g(n)). to be clear, I'm taking about little o It is possible with that information given to me, that f(n)=Omega(g(n)). To me it sounds that it's not possible, since Little-o definition says to me that…
Assaf
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how to prove f(n)=Θ(g(n)) => f(n)=cg(n)+o(g(n))

The question is to prove if the following is true or false. f(n) = Θ(g(n)) => f(n) = cg(n) + o(g(n)), for some real constant c > 0. note: the o is little oh I was trying to do the following: o(g(n)) means
swordgit
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When does one typically prefer the little-o instead of the big-O?

I understand the difference between the Big-O and the little-o, however I wonder when/why one would choose the little-o over the big-O for a particular situation (and the opposite).
Kevin Van Ryckegem
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CLRS exercise 3.2-4 Big-Oh vs Little Oh

I'm self studying CLRS, and I've hit this point - the question I'm answering is: Is the function ⌈lglgn⌉! polynomially bounded? And I've reduced it down to =Θ(lglgn⋅lglglgn) Now, all the solutions manuals seem to use little oh at this point to…
Verlet64
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Does little-o and little-omega have upper/lower bounds?

I know that Big-O defines upper bound and Big-Omega defines lower bound. I could not find information on Google whether Little-o and Little-Omega also defines upper/lower bounds. I read they have tight bounds, but does that mean they also define…
Mr.Rabbit
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Comparing complexities

I have these three questions for an exam review: If f(n) = 2n - 3 give two different functions g(n) and h(n) (so g(n) doesn't equal h(n)) such that f(n) = O(g(n)) and f(n) = O(h(n)) Now do the same again with functions g'(n) and h'(n), but this…
Jae
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Prove little-O from first principles

Prove that f(n) = 2010n^2 + 1388n belongs to o(n^3) Little-O Definition My work so far: This must be true: for ALL constats c>0, there exists a constant n0>0 such that 0<=2010n^2 + 1388n<=cn^3 for all n>n0 By simplifying we get: c>= 2010/n +…
NoName
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Trouble understanding little-o notation example

I'm having trouble with this one problem 9n <= cn^3 basically I can get down to 9/c <= n^2 But how do I solve the rest?
Frightlin
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Algorithm for Broken Priority Queue

IF a priority queue has two operations: insert and broken_min. Where broken_min returns either the first or second minimum item. These cannot both be implemented in o(logn) time. I think this is because insert uses broken_min and would then have to…
user3196347
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Can someone explain why f(n) + o(f(n)) = theta(f(n))?

According to this page: The statement: f(n) + o(f(n)) = theta(f(n)) appears to be true. Where: o = little-O, theta = big theta This does not make intuitive sense to me. We know that o(f(n)) grows asymptotically faster than f(n). How, then could…
user2445455
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Proving a given function equals o(N)

I am trying to prove that for any constant,k, log^k N = o(N) (little O of N) All that I know for little o is that it follows the form T(n) = o(p(n)) where T(n) grows at a rate slower than p(n). Also I can't really do a limit and use L'hopital rule…
user1251302
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