Talk:Big O notation
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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
Reinstated my VERY bad. Missed a bracket
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.
The section "The Hardy–Littlewood definition" contains this sentence:
- Hence is the negation of , and the negation of .
- In the classical (number theory) notation, f(x)<o(g(x)) means that f(x)<h(x), for some h(x)=o(g(x)), and f(x)≤o(g(x)) means that f(x)≤h(x), for some h(x)=o(g(x)): so the two notations are exactly equivalent.
- Regarding references for the notations , I put Ivić 1985 book, but this is not very satisfactory. I recall I used this notation much before 1985 (it was for instance systematically used by the number theory group at Urbana-Champaign in the late 70s), but I have been unable to find who actually used it first.Sapphorain (talk) 08:34, 31 August 2015 (UTC)