Maximum branching: Difference between revisions
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'''Definition:''' | '''Definition:''' | ||
A '''branching''' is a cycle-free directed graph such that each node has at most one incoming arc. | A '''branching''' is a cycle-free directed graph such that each node has at most one incoming arc. | ||
'''Input:''' | '''Input:''' | ||
# A directed graph <math>G=(V,A)</math>: | # A directed graph <math>G=(V,A)</math>: | ||
# A real-valued weight <math>w(a)</math> for each arc <math>a\in A</math>. | # A real-valued weight <math>w(a)</math> for each arc <math>a\in A</math>. | ||
'''Output:''' | '''Output:''' | ||
A branching of maximum weight such that all arcs in the branching are arcs of <math>G</math>. In that, the weight of a branching is the sum of the weights of all of its arcs. | A branching of maximum weight such that all arcs in the branching are arcs of <math>G</math>. In that, the weight of a branching is the sum of the weights of all of its arcs. | ||
Revision as of 08:51, 11 October 2014
General information
Definition: A branching is a cycle-free directed graph such that each node has at most one incoming arc.
Input:
- A directed graph [math]\displaystyle{ G=(V,A) }[/math]:
- A real-valued weight [math]\displaystyle{ w(a) }[/math] for each arc [math]\displaystyle{ a\in A }[/math].
Output: A branching of maximum weight such that all arcs in the branching are arcs of [math]\displaystyle{ G }[/math]. In that, the weight of a branching is the sum of the weights of all of its arcs.