scientific papers

 I'd say it in a bit different way: "The running time (performance might be a better term...) is far from the requirements of/for real applications."

I don't think an amount of time can be far away from an application.
Can you explain further what you mean by "a real application"? Are you referring to the amount of time required by some practical use of the algorithm? Something like that maybe?
CJ

Thanks for the reply. What I mean is:

the algorithm need to much time for small input, therefore, it can not be used in the real world applications.

Then you can say the algorithm's complexity is too high for it to be of practical value, or that it prevents it from being used in real applications. Use the term "performance" to refer to the running time with a given input size and "complexity" to denote the function of time vs. input size, which is traditionally calculated for any algorithm examined/analyzed.

I'm not sure that "complexity" is the best word here. Most people would understand it to mean "complicated", but an algorithm can be extremely complicated and yet still very fast; much faster, in fact, than simpler brute-force methods. How about: "There is an algorithm, but it is too inefficient to be of practical use."

the algorithm needs too much time for small input, therefore, it can not be used in the real world applications.

OK. In that case, I would change your original
Indeed, the running time is still far away from real applications.
to
Indeed, the run time is

thanks for all the replies. Now a new question. Is this sentence ok?

The proof follows exactly the lines of the proof of Lemma 3.

Daxiaoaixad

Daxiaoaixadthanks for all the replies. Now a new question. Is this sentence ok?

The proof follows exactly the lines of the proof of Lemma 3.

Daxiaoaixad

It looks OK to me.

Mr WordyI'm not sure that "complexity" is the best word here.

Complexity is a specific term familiar to most IT specialists. The complexity of an algorithm is a function of the input length (n) such that the limit of the ratio of this function and the real running time against this input, with n striving to infinity, is some finite non-zero number.
For exa