Can we determine which algorithm runs faster just by looking at their asymptomatic rate?

Question

Ok so lets say that the asymptotic execution time of an algorithm B is greater than the asymptotic execution time of an algorithm A .

Τ(Ν)Β = c1*f(N)B > Τ(Ν)A = C2*f(N)A for c1 and c2 that make the equals statement true

Can we say that as n(input) increases , A will run faster than B?

I'm new here , so forgive me if I got the tags wrong, thanks for your time!

"asymptomatic" refer to some illness, because it means "without symptom(s)" ; you probably mean "asymptotic." — Jean Marie, Jun 21 '17 at 14:50

score 1 · Accepted Answer · answered Jun 21 '17 at 14:44

1

If the execution time of $A$ is asymptotically smaller than $B$, it means that for sufficiently large input size $n$, $A$ is faster than $B$. More rigorously, there exists a positive integer $N$ such that, for all input size $n\geq N$, $A$ runs faster than $B$.

answered Jun 21 '17 at 14:44

Yining Wang

1,279
7
23

What if f(n)A and f(n)B are fixed functions and they both have execution times of 0(1) ? – Makis Mandrelas Jun 21 '17 at 14:50
If both algorithms have execution time $O(1)$, then neither is asymptotically faster than the other. – Yining Wang Jun 21 '17 at 14:54
In these problems the running times are only specified up to a multiplicative constant, so the two have to be different functions to say one is larger. – Ross Millikan Jun 21 '17 at 14:54
Thanks a lot for your time! – Makis Mandrelas Jun 21 '17 at 14:54

Can we determine which algorithm runs faster just by looking at their asymptomatic rate?

1 Answers1