On the Complexity of Submodular Function Minimisation on Diamonds

Abstract

Let (L;⊓,⊔) be a finite lattice and let n be a positive integer. A function f : L → R is said to be submodular if f(a ⊓ b) + f(a ⊔ b) ≤ f(a)+f(b) for all a, b ∈ L. In this paper we study submodular functions when L is a diamond. Given oracle access to f we are interested in finding x ∈ L such that f(x) = miny∈Ln f(y) as efficiently as possible. We establish… (More)
DOI: 10.1016/j.disopt.2011.04.001

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