1 research outputs found
New Query Lower Bounds for Submodular Function Minimization
We consider submodular function minimization in the oracle model: given
black-box access to a submodular set function , find an element of using as few queries to
as possible. State-of-the-art algorithms succeed with
queries [LeeSW15], yet the best-known lower bound has never
been improved beyond [Harvey08].
We provide a query lower bound of for submodular function minimization,
a query lower bound for the non-trivial minimizer of a symmetric
submodular function, and a query lower bound for the non-trivial
minimizer of an asymmetric submodular function.
Our 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 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 for - mincut, even in a directed, weighted graph