# Talk:Big O notation

## Algorithms and their Big O performance

I'd like to put in some mention of computer algorithms and their Big O performance: selection sort being N^2, merge sort N log N, travelling salesman, and so on, and implications for computing (faster computers don't compensate for big-O differences, etc). Think this should be part of this write-up, or separate but linked?

I think separate would be better, to increase the article count :-). Then you can have links from the Complexity, Computation and Computer Science pages. Maybe you can call it "Algorithm run times" or something like that. --AxelBoldt
Or something like analysis of algorithms or Algorithmic Efficiency since you may sometimes choose based on other factors as well. --loh
I'd recommend puting it under computational complexity which earlier I made into a redirect to complexity theory. It should be a page of it's own, but I didn't want to write it ;-) --BlckKnght

## Removed polylogarithmic

Reinstated my VERY bad. Missed a bracket

## "Tight" bounds?

The article refers to terms "tight" and "tighter", but these terms are never defined! Alas, other pages (e.g. "bin packing") refer to this page as the one giving a formal definition of this term; moreover, "Asymptotically tight bound" redirects here. Yes, the term is intuitively clear, but a math-related page should have clear definitions.

I think a short section giving a formal definition of the term "tight bound" and referring to Theta-notation is needed (e.g. as a subsection of section "8. Related asymptotic notations"), and once such a section is created the redirection from "Asymptotically tight bound" should link directly there.

## ⊂

Near the end of the section titled Little-o notation the right facing "U" is used as follows:

```o ( f ) ⊂ O ( f ) {\displaystyle o(f)\subset O(f)} o(f)\subset O(f) (and thus the above properties apply with most combinations of o and O).
```

However the Set (mathematics) page under Subsets says,

"The expressions A ⊂ B and B ⊃ A are used differently by different authors; some authors use them to mean the same as A ⊆ B (respectively B ⊇ A), whereas others use them to mean the same as A ⊊ B (respectively B ⊋ A)."