Maximum spanning forest: Difference between revisions
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== Input == | == Input == | ||
# An [[undirected graph]] <math>G = (V,E)</math>, not necessarily connected. | # An [[Basic graph definitions#Directed and undirected graphs|undirected graph]] <math>G = (V,E)</math>, not necessarily connected. | ||
# An edge length <math>l(e) \in \mathbb{R}_0^+</math> for each edge <math>e \in E</math>. | # An edge length <math>l(e) \in \mathbb{R}_0^+</math> for each edge <math>e \in E</math>. | ||
Revision as of 12:31, 16 June 2015
Input
- An undirected graph [math]\displaystyle{ G = (V,E) }[/math], not necessarily connected.
- An edge length [math]\displaystyle{ l(e) \in \mathbb{R}_0^+ }[/math] for each edge [math]\displaystyle{ e \in E }[/math].
Output
An undirected forest [math]\displaystyle{ F= (V,E_F) }[/math] such that [math]\displaystyle{ E_F \subseteq E }[/math].
Objective
Maximize: [math]\displaystyle{ \sum{}{}_{e \in E_F}l(e) }[/math].
Complexity
Polynomial.