Can the asymptotic expression $mathcal{O(log(n) cdot log(m))}$ be simplified?
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?
asymptotics
asked Nov 17 at 11:20
3nondatur
350111
add a comment |
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?
asymptotics
asked Nov 17 at 11:20
3nondatur
350111
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
add a comment |
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?
asymptotics
asked Nov 17 at 11:20
3nondatur
350111
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
asymptotics
asked Nov 17 at 11:20
3nondatur
350111
asked Nov 17 at 11:20
3nondatur
350111
asked Nov 17 at 11:20
3nondatur
350111
asked Nov 17 at 11:20
3nondatur
350111
asked Nov 17 at 11:20
3nondatur
350111
350111
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
add a comment |
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
add a comment |
1 Answer
1
active
oldest
votes
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.
answered Nov 17 at 11:23
Matt Samuel
36.1k63463
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
answered Nov 17 at 11:23
Matt Samuel
36.1k63463
add a comment |
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.
answered Nov 17 at 11:23
Matt Samuel
36.1k63463
add a comment |
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.
answered Nov 17 at 11:23
Matt Samuel
36.1k63463
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.
answered Nov 17 at 11:23
Matt Samuel
36.1k63463
answered Nov 17 at 11:23
Matt Samuel
36.1k63463
answered Nov 17 at 11:23
Matt Samuel
36.1k63463
answered Nov 17 at 11:23
Matt Samuel
36.1k63463
36.1k63463
add a comment |
add a comment |
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3002234%2fcan-the-asymptotic-expression-mathcalologn-cdot-logm-be-simplified%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
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