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We consider submodular function minimization in the oracle model: given black-box access to a submodular set function $f:2^{[n]}rightarrow mathbb{R}$, find an element of $argmin_S {f(S)}$ using as few queries to $f(cdot)$ as possible. State-of-the-art algorithms succeed with $tilde{O}(n^2)$ queries [LeeSW15], yet the best-known lower bound has never been improved beyond $n$ [Harvey08]. We provide a query lower bound of $2n$ for submodular function minimization, a $3n/2-2$ query lower bound for the non-trivial minimizer of a symmetric submodular function, and a $binom{n}{2}$ query lower bound for the non-trivial minimizer of an asymmetric submodular function. Our $3n/2-2$ lower bound results from a connection between SFM lower bounds and a novel concept we term the cut dimension of a graph. Interestingly, this yields a $3n/2-2$ cut-query lower bound for finding the global mincut in an undirected, weighted graph, but we also prove it cannot yield a lower bound better than $n+1$ for $s$-$t$ mincut, even in a directed, weighted graph.
Submodular function minimization (SFM) is a fundamental discrete optimization problem which generalizes many well known problems, has applications in various fields, and can be solved in polynomial time. Owing to applications in computer vision and m
This paper bridges discrete and continuous optimization approaches for decomposable submodular function minimization, in both the standard and parametric settings. We provide improved running times for this problem by reducing it to a number of cal
It has been observed independently by many researchers that the isolating cut lemma of Li and Panigrahi [FOCS 2020] can be easily extended to obtain new algorithms for finding the non-trivial minimizer of a symmetric submodular function and solving t
In this paper we provide improved running times and oracle complexities for approximately minimizing a submodular function. Our main result is a randomized algorithm, which given any submodular function defined on $n$-elements with range $[-1, 1]$, c
We study problems with stochastic uncertainty information on intervals for which the precise value can be queried by paying a cost. The goal is to devise an adaptive decision tree to find a correct solution to the problem in consideration while minim