Talk:Hopcroft–Karp algorithm/Archive 1

Archive 1

Untitled

This needs an explanation of the "run really fast" step (http://www.fysh.org/~katie/computing/methodologies.txt)

I don't understand the comment. --a3nm (talk) 10:48, 4 April 2020 (UTC)

Delta

Is $N\Delta P$ the only standard terminology we can use? I would prefer to leave $\Delta$ to the maximum degree of the graph. Adking80 (talk) 22:06, 18 July 2008 (UTC)

I have seen $N\oplus P$ (symmetric difference) used in several papers. It seems a much better notation to me. Also, the meaning of $\Delta$ is not explained on the page. I have updated the page accordingly. —Preceding unsigned comment added by Michael Veksler (talk • contribs) 22:29, 9 October 2008 (UTC)

Shortestest

Is shortestest a word? ;D User:Ozzie (talk) 20:37, 7 March 2008 (UTC)

Seems outdated. --a3nm (talk) 10:48, 4 April 2020 (UTC)

Maximum vs. maximal

Changed the incorrect "maximum" to "maximal". —Preceding unsigned comment added by 80.145.225.62 (talk • contribs) 22:44, 3 October 2006 UTC

I agree. Thanks for persisting after the incorrect revert. —David Eppstein 05:55, 4 October 2006 (UTC)

I am sorry for the incorrect revert. I now think that I was wrong. I started this article because the algorithm was mentioned in the text of another article. The only reference I had was CLRS, where it said maximum. So when I saw this edit from an unregistered user, I checked in CLRS, saw that it said maximum, and assumed that the editor was either in error or mischevious. Sorry about this. Let me check that we agree with terminology:

If we go through a one-dimmensional state-space (x-axis below), where each state has a value (y-axis below),

           B                                                                   
           /\                                                                  
   A      /  \                                                                 
   /\    /    \                                                                
  /  \  /      \                                                               
 /    \/        \                                                              
/                \

then here both A and B are maximal points, while only B is a maximum. This is the terminology used in the article Matching.

The description in CLRS is actually just given as an exercise. I tried to solve it, but could not see how to find "maximum set of vertex-disjoint shortest augmenting paths" in $O(V+E)$, so I just wrote the pseudocode for the algorithm as described, and put it in my ever-growing TODO to figure out the missing part. I now found a description of the pseudo-code which still says maximum in the comments, but the code clearly gives only something maximal. So the problem was simpler than I thought :) Thanks for the correction, and sorry about my error. Klem fra Nils Grimsmo 09:16, 4 October 2006 (UTC)

Difference from Dinic algorithm (Dinits' algorithm)?

What's the difference between this algorithm and Dinic algorithm? To me, it just looks like Dinic algorithm - only run on a specific input, so it has better time complexity than general-case Dinic. --Lukas Mach 22:27, 27 December 2006 (UTC)

It's none... H-K is 1973 algorithm and Dinic is 1976 algorithm. --Lukas Mach 01:55, 26 February 2007 (UTC)

Added mention of Dinic's algorithm on the page. --a3nm (talk) 10:48, 4 April 2020 (UTC)

Another estimations

Another estimations are O((V+E)V ^1/2) and O(V ^5/2): Lipski W., Kombinatoryka dla Programistow, [Combinatorics for Programmers], Wydawnictwa Naukowo-Techniczne, Warzawa, 1982.--Tim32 (talk) 10:58, 19 November 2007 (UTC)

Both bounds are worse. We can assume that every vertex is incident to at least one edge, so $V+E=O(E)$. We also know that $E<V^{2}/2$. Adking80 (talk) 22:04, 18 July 2008 (UTC)