Maximum matching by Edmonds: Difference between revisions
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'''Break condition:''' | '''Break condition:''' | ||
There is no more [[Matchings in graphs#Alternating and augmenting paths|augmenting path]]. | There is no more [[Matchings in graphs#Alternating and augmenting paths|augmenting path]]. | ||
'''Definition:''' | |||
A '''blossom''' is a cycle <math>C</math> of odd lengths in <math>G</math> such that <math>\lfloor|C|/2\rfloor<\math> edges on <math>C</math> are matched and the remaining node is matched as well. | |||
== Induction basis == | == Induction basis == | ||
Revision as of 13:20, 21 November 2014
Abstract view
Invariant: The current selection [math]\displaystyle{ M }[/math] of edges is a matching.
Variant: Either the cardinality of [math]\displaystyle{ M }[/math] increases, or the number of nodes of [math]\displaystyle{ G }[/math] decreases.
Break condition: There is no more augmenting path.
Definition: A blossom is a cycle [math]\displaystyle{ C }[/math] of odd lengths in [math]\displaystyle{ G }[/math] such that [math]\displaystyle{ \lfloor|C|/2\rfloor\lt \math\gt edges on \lt math\gt C }[/math] are matched and the remaining node is matched as well.
Induction basis
Abstract view: Start with some matching, for example, the empty matching.
Induction step
Apply the