TLO5 �������&aacu

If the edges of the graph have an associated weight

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: : 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:
View Full Document

Ask a homework question - tutors are online