Talk:Van Emde Boas tree

message: Is this structure really known as the vEB tree, with a lowercase v? In Dutch last names written separately, initial prepositions or articles are capitalized, thus:
* Peter van Emde Boas
* Van Emde Boas, Peter
* meneer Van Emde Boas (mister VEB)
Qwertyus 01:16, 21 July 2006 (UTC)
replies: text: They are popularly called vEB trees in many other sources that I've seen, which I'm pretty sure predate this article. This may not be technically correct, but it seems to be conventional. I don't know whether the lowercase v is used when the name is spelled out in full. Deco 01:48, 21 July 2006 (UTC)

text: I've changed it to Van Emde Boas tree since that seems common enough.. With a lowercase initial letter, it just looks too strange. Qwertyus (talk) 12:19, 22 June 2012 (UTC)
replies: text:  Usually spelled  van Emde Boas Trees, see van Emde Boas Trees - Stanford University or van Emde Boas Trees (vEB trees) 185.176.78.179 (talk) 07:51, 4 June 2019 (UTC)
thread_title: van or Van?

message: findNext returns always only ".min" values, never ".max"...
What if the value we are searching for is stored in some .max field?
(E.g. the tree contains values 34 and 47 and none between them, 47 is stored in some .max field, and "findNext(38)" is called.)  —Preceding unsigned comment added by 80.95.85.174 (talk) 22:01, 7 October 2009 (UTC)
thread_title:  .max is never returned by findNext 

message: I cannot find anywhere on the net about how to pronounce Van Emde Boas. Can someone add the IPA into the article? --112.118.153.103 (talk) 03:46, 12 July 2010 (UTC)
replies: text: I added my best shot. QVVERTYVS (hm?) 15:27, 7 March 2014 (UTC)
thread_title:  How to pronounce? 

message: I think, it would be easier to read, if the letter m was changed to w, which is the conventional letter for "word length".
Gabriel (talk) 15:26, 13 May 2011 (UTC)
thread_title:  Change letter 

message: There's a bug in insert function when T.min<T.max<x
The T.max won't be updated
Please fixTheme (talk) 03:13, 13 March 2013 (UTC)
replies: text: You were absolutely right. I just implemented the pseudocode in C++ and it lost elements every time the subtree was assigned a new value. The code worked just fine after modifying the code like you suggested. I will correct the pseudocode in the article right away. Kilgore T (talk) 07:57, 19 July 2018 (UTC)
thread_title:  Bug in insert function 

message: I can't find anything that talks about the initial values of T.min and T.max  Theme (talk) 03:13, 13 March 2013 (UTC)
thread_title:  Initial values 

message: if T.aux is empty then
            T.min = T.max
            return
        if T.aux is empty then
            T.max = T.min
            return
This fragment of code is unreachable because if T.aux is empty, the only element in the tree is min, so min=max and is caught in the first ifTheme (talk) 03:13, 13 March 2013 (UTC)
thread_title:  unreachable code in delete function 

message: When the only data in the tree are T.min and T.max, and x==T.max, T.children[T.aux.max].max will be T.max, so T.max=T.children[T.aux.max].max is incorrectTheme (talk) 03:20, 13 March 2013 (UTC)
thread_title:  Bug in delete function 

message: It would be nice to read something about practical applications of the tree.
Maybe some software that uses it?  — Preceding unsigned comment added by Michael.lill (talk • contribs) 11:32, 1 June 2017 (UTC)
thread_title:  Practical applications 

message: I just fixed the pseudocode bugs in 'insert' and 'delete' previously reported here. I tested the original version with a C++ program and gave wrong results for both operations. The fixed version correctly applied the two operations. Kilgore T (talk) 08:19, 19 July 2018 (UTC)
thread_title:  Fixed two bugs in insert and delete 

message: In section "Similar structures", the article states that by replacing the arrays in the data structure with hash tables, one can reduce the space to O(n). Although this was believed to be the case for some time and and a CLRS (ed. 3) exercise asks for a proof of this, the actual worst case space bound is O(n \log m). This bound is proved in https://v.cunat.cz/theses/master.pdf (page 29 f.) by proving an upper bound and a matching lower bound. That the O(n) bound is incorrect is also mentioned in the CRLS errata (https://www.cs.dartmouth.edu/~thc/clrs-bugs/bugs-3e.php).
It is possible to achieve O(n) using hash tables, but this requires an additional technique of dividing the elements into groups of size \Theta(\log m) (the thesis above also proves this on page 33 f.). However, this is additional technique is not mentioned by the (Wikipedia) article. Sith98 (talk) 09:09, 30 May 2023 (UTC)
replies: text: I updated the space bound in the article text. The lower bound counterexample is really simple: just use a set of numbers whose low-order bits are all zero, as far up as possible for how many there are, so that everything goes into the high-halfword structure and then recurses in the same way. —David Eppstein (talk) 17:45, 30 May 2023 (UTC)
thread_title:  Incorrect space requirement for vEB trees with hash tables