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I am writing a paper in which I want to refer to a group of algorithms. Some of these algorithms are of complexity O(NlogN), and some of the are more complex (e.g polynomial-time) and I want to refer to them all in one term. Is there any common term to use in such a situation?

linearithmic refers to O(NLOGN) algorithms and it's narrower than what I'm looking for. I don't think of non-linear as a good term to use here. If it is, then correct me please.

my sentence:

In such a setting, state-of-the-art community-detection algorithms does not scale well. To reduce the running time of these XYZ algorithms, each sub-graph is partitioned into chunks.

I want to change `XYZ' in the above, to what I am asking for.

ameerosein
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3 Answers3

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As mentioned by Bryce Kille in the comments, superlinear is what you are looking for. From Wiktionary:

  1. (mathematics) Describing a function that eventually grows faster than any linear one

(By the way, the first phrase in your question strikes me as rather odd: "[...] I want to refer to a group of algorithms that are mostly polynomial-time, but one of them is of complexity $O(N \log N)$." Do you simply mean "linear" instead of "polynomial-time"?)

dkaeae
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On top of the other answers, you can also say $\omega(n)$ and people should know what you mean, but often won't.

Pseudonym
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I want to refer to a group of algorithms that are mostly polynomial-time, but one of them is of complexity O(NlogN). Is there any common term to use in such a situation?

Yes: polynomial. Note that $O(N \lg N) \subset O(N^2)$.

I am trying to mention that these algorithms' running time grow faster than linear.

That makes them superlinear. If you want to be explicit about the fact that you're talking about the intersection you could say superlinear polynomial.

Peter Taylor
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