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If the edges of the graph have an associated weight

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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 other subset. Matching in bipartite graphs can be computed efficiently as an assignment problem. Source: http://en.wikipedia.org/wiki/Bipartite_graph...
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