8.438 Advanced Combinatorial Optimization 2 Iwata and Orlin's Algorithm
نویسنده
چکیده
Given a finite set V with n elements, a function f : 2 → Z is submodular if for all X,Y ⊆ V , f(X ∪ Y ) + f(X ∩ Y ) ≤ f(X) + f(Y ). Submodular functions frequently arise in combinatorial optimization. For example, the cut function in a weighted undirected graph and the rank function of a matroid are both submodular. Submodular function minimization is the problem of finding the global minimum of f . It is polynomial time solvable (assuming that f can be efficiently computed), as it was shown by Grötschel, Lovász and Schrijver [2] using the ellipsoid method. In this lecture, we describe a recent efficient combinatorial algorithm for submodular function minimization by Iwata and Orlin [1].
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