Graphic Submodular Function Minimization: A Graphic Approach and Applications
نویسندگان
چکیده
We develop an efficient and conceptually simple algorithm for minimizing the sum of the rank-function of a graph G = (V,E) and of a linear function on E. We call such set-functions “graphic submodular”. The algorithm we present for graphic submodular function minimization is a greedy algorithm consisting of |V | − 1 steps, where the steps require the solution of a network flow problem on subgraphs (with slight modifications) induced by 2, . . . , |V | vertices of the given graph. We also point at various alternatives for solving this problem in polynomial time and their interconnections, as well as variants of the problem itself. Motivated by applications, we also show how this direct approach to graphic submodular function minimization provides efficient solutions for some derived problems.
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