Approximating Submodular Matroid-Constrained Partitioning
The submodular partitioning problem asks to minimize, over all partitions P of a ground set V, the sum of a given submodular function f over the parts of P. The problem has seen considerable work in approximability, as it encompasses multiterminal cuts on graphs, k-cuts on hypergraphs, and elementary linear algebra problems such as matrix multiway partitioning. This research has been divided between the fixed terminal setting, where we are given a set of terminals that must be separated by P, a…
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