Unformatted text preview: : http://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg Matching
• Matching – A matching in a graph G=(V, E) is a subset M of the edges E such that no two
edges in M share a common end node.
– A perfect matching M in G is a matching such that each node of G is incident to
an edge in M.
– If the edges of the graph have an associated weight, then a maximum (minimum)
weighted perfect matching is a perfect matching such that the sum of the
weights of the edges in the matching is maximum (minimum).
– There is a complicated but polynomial-time algorithm (Babow, 1975; Lawler, 1976)
for finding a minimum weight perfect matching.
– A simpler case (Bipartite weighted matching)
• A graph is bipartite if it has two mutually exclusive and complete subsets of nodes and
the edges are only allowed between nodes of different subsets.
A matching in a bipartite graph therefore assigns nodes of one subset to nodes of the
Matching in bipartite graphs can be computed efficiently as an assignment problem. Source: http://en.wikipedia.org/wiki/Bipartite_graph...
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- Summer '10
- Graph Theory, Bipartite graph, Daganzo, Terminal Location Problem