Talk:Master theorem (analysis of algorithms)

message: Where did the term "master theorem" originate?
CLRS cites Bentley, Haken, and Saxe (1980)
for the theorem, but the article by Bentley et al. does not use the term
"master theorem".  —Preceding unsigned comment added by 128.151.39.160 (talk) 17:02, 12 May 2011 (UTC)
thread_title:  Origin of term 

message: Looking into other sources about the issue, I find no reference for the exact stating of the "Case 2" given here.
Instead it appears to be described everywhere as the special case of (k=0).
Could it be that there is a mistake here? or is it that all other places are less general forms?
Having looked into Cormen's book, I see the same there: no 'k' mentioned in the second case's context.
Reference:
http://www.cs.concordia.ca/~chvatal/notes/master.pdf
http://www.columbia.edu/~cs2035/courses/csor4231.F03/recurrences.pdf
and many others.
Seftembr 23:32, 1 December 2006 (UTC)
replies: text: The Case 2 showed here is exactly the one from the Goodrich-Tamassia book. I have added that reference to the article. —David Eppstein (talk) 00:42, 25 February 2009 (UTC)
thread_title:  Case2 skepticism 

message: I believe there should be "The" in from of "Master theorem". In either case, can someone at least redirect it to here?  As it currently stand, if you search "The Master Theorem", this page will actually NOT show up as a result!
24.222.8.32 17:33, 5 December 2006 (UTC)
thread_title:  Page Title Change: The Master Theorem 

message: I have read many wikipedia pages that describe mathematical theorems. and many are very obtuse, and usually digress in many directions preventing the main idea from being conveyed. This article is of utmost excellence. And did a better job describing the theorem than my college book or professor. If any content is to be added, please make sure it is added below the existing content. The original content is very explanatory and the examples are very thourough and excellently explained. Some of the final answers where in a font rather small and hard to see on a 1024x768 resolution (please verify if this is a problem on other browsers) but otherwise, this is the most concise article on a mathmatical theorem i have read on wikipedia. It's greatness is in it's simplicity. Please do not dilute it, and keep up the good work! —The preceding unsigned comment was added by Jediborg (talk • contribs) 05:46, 20 February 2007 (UTC)
thread_title:  Excellent job 

message: This theorem is all well and good, but it just sits in space providing no reason why anyone would want to use it.  It would be much better if an example or description of its relevance to the world, or mathematics was added.  Centroyd
 I feel the same way, studying it right now for a class!
:Disagreed, the first sentence of the article gives exactly what you ask for. A.N. Yzelman 08:34, 21 June 2007 (UTC)
thread_title:  Relevance and Examples 

message: Also, does it really make sense to put this under 'Computer Languages' ?
:It does not, but it seems to have been resolved already. A.N. Yzelman 08:34, 21 June 2007 (UTC)
thread_title:  Category: Computer Languages 

message: The discussion of a/b should be n/b, at least as given in Cormen, Leiserson and Rivest 1st Ed. p62. Terrycojones 09:25, 26 Oct 2004 (UTC)
replies: text: Not sure which part you meant? Probably the error has already been corrected. A.N. Yzelman 08:34, 21 June 2007 (UTC)
thread_title:  a/b vs n/b 

message: I think that Special Cases should be discussed as well, as there are gaps between the cases. 66.130.236.213 19:13, 21 September 2006 (UTC)
thread_title:  Special Cases 

message: I assume it needs to be rewritten. Some portion of this page is to be removed and some more descriptive portion is to be added.
Nafsadh (talk) 20:21, 30 December 2007 (UTC)
thread_title:  Meet quality 

message: This writing is probably not correct (not only in this special case):
:T(n) = \Theta\left( n^{\log_b a} \right)
Theta represents a set of functions and T(n) is only a special function of these it should rather be written
:T(n) \in \Theta\left( n^{\log_b a} \right)
Though the first writing is commonly used, the second is mathematically correct and the first is not, because a set of functions(N->R) can not equal a single function(N->R)
95.223.140.220 (talk) 22:56, 4 July 2009 (UTC)
replies: text: It is not for us here to promote nonstandard notation. "=Θ" is the standard notation for "has the same order of magnitude as", a relation between two functions rather than a membership relation between a function and a set. It is perfectly valid mathematically as long as one regards "=Θ" as being a single compound symbol rather than as two separate = and Θ symbols. The other notation is much less standard and should be avoided for that reason, logical though it may be. —David Eppstein (talk) 23:13, 4 July 2009 (UTC)

text: It is not very helpful that both versions are used inconsistently throughout the article. I'd be fine if everything was "=Θ" but it's not. I prefer the element version as it's more accurate semantically, though I agree that more people may use the other one for simplicity. Just be consistent. In any case, please don't call people pedantic when reverting changes. —Xiphoseer (talk) 14:32, 18 July 2017 (UTC)
thread_title:  Formal correctness 

message: One example in section Inadmissible states:
"T(n) = 2T\left (\frac{n}{2}\right )+\frac{1}{n}.
There does not exist a c < 1 such that 2\frac{2}{n} \le c\frac{1}{n}."
However, the explanation is inconsistent with the description of Case 3 of the master theorem. 
I suspect this was just a simple inversion typo and that the explanation should read:
"There does not exist a c < 1 such that 2\frac{n}{2} \le c\frac{1}{n}."
What do you think?
smt (talk) 23:35, 3 November 2009 (UTC)
thread_title:  Error in inadmissible example? 

message: Inadmissible equations says "... cannot be solved using the master theorem".
Isn´t it the case that you can solve
T(n) = 2^nT\left (\frac{n}{2}\right )+n^n 
by the substitution S(n) = \frac{T(n)}{2^{2n}}  to get 
T(n)/2^{2n} = T\left (\frac{n}{2}\right )/2^n + (\frac{n}{4})^n or equally
S(n) = S\left (\frac{n}{2}\right ) + (\frac{n}{4})^n 
and, with Master Theorem case 3 under the condition 
(n/8)^{n/2} \le c\cdot (n/4)^n 
which is true almost everywhere for arbitrary choosen constant 0<c<1, you get 
S(n) = \Theta\left ((\frac{n}{4})^n\right ).
This leads to the asymptotic term T(n) = \Theta(n^n) by using the Master Theorem I think.
Joerg Bader (talk) 00:33, 18 February 2011 (UTC)
thread_title:  Inadmissible equation? 

message: If f=0, then f is obviously O-big of anything. It is reasonable to expect that Theta=const=0 is also possible as a solution, but the theorem states that it can't be the case. Maybe it is missing somewhere the requirement that f>0? 80.237.26.14 (talk) 15:25, 27 July 2011 (UTC)
thread_title:  Case 1 formal note 

message: This is a snapshot of the Generic Form section, after my proposed changes: https://en.wikipedia.org/w/index.php?title=Master_theorem&oldid=785156913#Generic_Form Ninjagecko (talk) 06:11, 12 June 2017 (UTC)
thread_title:  Proposed changes 

message: This is a snapshot of the Generic Form section, before my proposed changes, to which the article is being reverted to: https://en.wikipedia.org/w/index.php?title=Master_theorem&oldid=784218527#Generic_form Ninjagecko (talk) 06:11, 12 June 2017 (UTC)
thread_title:  Prior state 

message: *Slightly violating the WP:MOS, even after editing for decades on WP, should not disqualify any edits, but attract some gnomes to rectify  certain violations of capitalizing, inappropriate direct addressing of readers, projecting anthropomorphism to theorems (is it allowed to have one such to state a proposition?), and other nitpicking like non-italicizing op-names.
*In a similar effort, those who feel themselves comfortable in their elaborate use of the English language as it is correctly spoken/written in WP, should be able to save the half step in sesquipedaling.
*Personally, I would like to avoid writing about some notation others use to be ridiculous, at least as long as the intention is reconstructible. Considering that even abusive notation is in heavy use, I suggest to check if editing out the ridicule improves the article.
*I consider color to be a design element, not available to Gutenberg and his first successors, and still somewhat rare within books not intended for infantile readership, the good use of which greatly enhances intelligibility of complex content.
*Are there any non-formal objections to the proposed content?
Look, how could one rank form over function? Purgy (talk) 10:09, 12 June 2017 (UTC)
replies: text: I can't even get to what has changed in the function because the form is unreadable. And that includes being written in unreadable English, not just minor details of capitalization. —David Eppstein (talk) 14:38, 12 June 2017 (UTC)

text: Also, the new text "Whenever we have a recurrence of this form, we can consider it as occurring in one of three regimes" is objectively false. There are plenty of recurrences of this form that do not fall under any case of the theorem. —David Eppstein (talk) 06:18, 13 June 2017 (UTC)
replies: text:  I think that tables can be a good way of conveying some kinds of information, but in the present case every single entry in the table is itself a block of text -- there is no advantage created, you still have to read every single block of text to understand what it's saying, and reading small cramped blocks of text is harder than reading paragraphs.  I do not think the table is an improvement. (By contrast, the smaller table at the bottom of the article shows a place where a tabular presentation can allow for easy comparison by eye.) The redundant words-ful formulas are also terrible, they are helpful only if you already know what they mean -- the cleaner formula with a sentence explaining how to interpret its terms is much better.  I have not made any attempt to evaluate any smaller-scale edits.  --JBL (talk) 14:57, 13 June 2017 (UTC)

text:  P.S. Whatever way this gets resolved, the "See also" section is in a very weird place and will need to be relocated.  --JBL (talk) 15:02, 13 June 2017 (UTC)
replies: text:  I have tried to work in some of your feedback about the verbosity of the regime table, and the textual equation, and some other concerns of David Eppstein's in the following edit. https://en.wikipedia.org/w/index.php?title=Master_theorem&oldid=785547309 Ninjagecko (talk) 04:46, 14 June 2017 (UTC)
thread_title:  Discussion 

message: How is binary tree traversal complexity C(n) = 2 C(n/2) + O(1)? Is the tree assumed to be almost complete to have both sides of size n/2?  — Preceding unsigned comment added by Quentin Fortier (talk • contribs) 09:22, 17 September 2017 (UTC)
thread_title:  Binary tree traversal	 

message: In the pseudocode we have the statement: if n < some constant k.
This can be confused with the k in case examples under the section of Generic form when glancing through the article.
Dizqar (talk) 15:04, 1 May 2021 (UTC)
thread_title:  Small note on usage of k 

message: This phrase does not make sense:
"T(n) = Theta(1) when n is less than some bound kappa".
If n is bounded then asymptotic stuff about a function of n don't make sense.
Just say "T(n) is bounded" instead of "T(n) = Theta(1)". 2601:985:4380:C00:980B:EA88:5DB3:A164 (talk) 15:08, 2 November 2022 (UTC)
thread_title:  Minor glitch in use of Big Theta