An algorithm for computing the matching capacity

R. Ahlswede and N. Cai [Information and control: matching channels, IEEE Trans. Inform. Theory 44 (2) (1998) 542-563] studied the asymptotic behavior of matching numbers ν(G⊗n) for the n-th powers of a bipartite graph G and proved the existence of the matching capacity γ(G)=limn→∞1nlogν(G⊗n). Moreover, they proved that γ(G)=maxmin(P,Q)∈K(G){H(P),H(Q)}, where H is the entropy function and K(G) is the set of König-Hall pairs of distributions defined in Section 2. In this paper an iterative method of computing the matching capacity of a bipartite graph G in which each vertex of degree ≥2 is adjacent to at least one vertex of degree 1 is presented and its exponentially fast convergence is shown.