Talk:Hungarian algorithm

message: The title of the "Theory" section is not quite right.  I can't see that it is any more theoretical than other sections.  What it does is that it decsribes the algorithm.  Unfortunately the description is not self-contained, and thus completely  unreachable for non-specialist. Actually the terse formulation and references to concepts not introduced (the matrix, prime zeros, etc) make me think that this is a violation of copyright (a paragraph taken from some larger work) Wazow 17:44, 4 March 2006 (UTC)
replies: text: This is an article on the Hungarian method, not a tutorial on Operations Research. The reader is assumed to have sufficient knowledge on the subject in order to understand what it is about. Terms such as 'matrix' and 'prime zeros' are no more copyrighted than 'algorithm', it's standard terminology on the topic, so I don't know what you're on about. Miskin 14:34, 24 March 2006 (UTC)

text: Actually I don't understand what you're talking about. To my knowledge there's no reference to any problems elsewhere. Again, you're asking a tutorial on optimization, which is beyong the scope of the article (for the obvious reasons). Miskin 14:34, 24 March 2006 (UTC)

text: Answering my question: the lines of the matrix stand for the first vertex set, and the columns stand for the second vertex set. Bender05 13:16, 24 March 2006 (UTC)

message: Am I the only one who feels that textual references to rows and columns correspond to columns and rows in the diagrams? That is: we are reading rows when we mean columns, and vice versa. We are directed to 'Mark all rows having no assignments (row 1),' but isn't it column 1 that lacks a clear—ie, unambiguous—assignment, due to its containing two zeros?
I could easily be mistaken about this, because it's a long time since I learned the Hungarian Method. I'll see how things look after a review of my old notes! Aboctok (talk) 21:32, 20 May 2011 (UTC)
thread_title:  Matrix Interpretation—Step 3 

message: I feel that the algorithm as presented is incorrect. Suppose we try to perform it on the following matrix:
\begin{pmatrix}
 0'& 0 & 1\\
1& 0'& 0\\
0 & 1 & 1\end{pmatrix}
Then we first mark row 3, then column 1, then row 1. Then we end up drawing two lines: through row 2 and column 1. This clearly does not cover all of the zeros.  — Preceding unsigned comment added by Batconjurer (talk • contribs) 12:00, 12 February 2018 (UTC)
thread_title:  Matrix Interpretation-Step 3 

message: Page says "however Edmonds and Karp, and independently Tomizawa noticed that it can be modified to achieve an O(n^3) running time." Is there a citation for this?  — Preceding unsigned comment added by 87.212.207.8 (talk) 14:06, 27 April 2016 (UTC)
thread_title:  n^3 time 

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thread_title:  External links modified 

message: The algorighm in step 3 is not true to all of the matrixes.  — Preceding unsigned comment added by 132.70.66.14 (talk) 13:18, 19 December 2017 (UTC)
thread_title:  step 3 

message: Section The_algorithm_in_terms_of_bipartite_graphs says:
(Precondition P:) "If {\displaystyle R_{T}\cap Z}R_T \cap Z is empty, then let " [...] (Note N:) "(note that the number of tight edges does not necessarily increase)." 
I can't believe that this Note N holds under Precondition P.
Also, the section "Proof that the algorithm makes progress" below says:
"that is, to either increase the number of matched edges, or tighten at least one edge"
I understand the "tighten at least one edge"-Part as exactly the Precondition-P-part from above !?
(Also I assume the "increase the number of matched edges" probably relates to "If {\displaystyle R_{T}\cap Z}R_T \cap Z is nonempty..." from above?)
As you can infer, I am missing some connections... the "If {\displaystyle R_{T}\cap Z}R_T \cap Z is nonempty"-Part should be labeled something like "augmenting case", so that it could be related better to that mentioned corresponding part in the proof; or Z could be introduced as something like "the set of nodes that could possibly participate in an augmentation path", with relation to Berge's Lemma, to help unterstanding the purpose of Z from the start on.
Fjf2002 (talk) 19:26, 14 March 2021 (UTC)
thread_title:  The_algorithm_in_terms_of_bipartite_graphs, possible error? "(note that the number of tight edges does not necessarily increase)" 

message: In step 3 it says "Repeat this till a closed loop is obtained." What is meant by loop? We just have a matrix with zero and nonzero elements. (I know a different algorithm where you have to "cover" all 0 by selecting a minimum number of rows and/or columns. You proceed by adding that row/col that removes a max. number of zeros not covered yet.) — MFH:Talk 15:03, 18 January 2024 (UTC)
thread_title:  "loop" in step 3?