Hungarian algorithm: Difference between revisions

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Cadduk (talk | contribs)
Undid revision 1144784037 by Cmglee (talk) The procedure does not use the same naming conventions as the rest of the article. The presented algorithm seems to not work every time, or the description is at least not complete (what if no row or column has a single 0 ?), this is not the one detailed in the article. It is very confusing without a detailed explanation of the steps.
B52481 (talk | contribs)
mark last step of matrix interpretation as unclear
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===Step 5===
 
{{Confusing|section}}
 
'''Find the lowest uncovered value. Subtract this from every unmarked element and add it to every element covered by two lines.'''
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If following this specific version of the algorithm, the starred zeros form the minimum assignment.
 
From Kőnig's theorem,<ref>[[K%C5%91nig%27s theorem (graph theory)]] Konig's theorem</ref> the minimum number of lines (minimum Vertexvertex cover<ref>[[Vertex cover]] minimum vertex cover</ref>) will be {{mvar|n}} (the size of maximum matching<ref>[[Matching (graph theory)]] matching</ref>). Thus, when {{mvar|n}} lines are required, minimum cost assignment can be found by looking at only zeroes in the matrix.
==Bibliography==
* R.E. Burkard, M. Dell'Amico, S. Martello: ''Assignment Problems'' (Revised reprint). SIAM, Philadelphia (PA.) 2012. {{ISBN|978-1-61197-222-1}}