Let G = (X ∪ Y, E) be a bipartite graph such that the vertices are partitioned into two groups X and Y , and each edge has one end point in X and one end point in Y . A 2-1 generalized matching is a set of edges S ⊂ E satisfying the following two conditions: 1. Every vertex in X belongs to at most two edges in S. 2. Every vertex in Y belongs to at most one edge in S. How do I give an algorithm to find the size (number of edges) of maximum 2-1 generalized matching?

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