A data-structure trick based on binary segment decomposition yields near-optimal ~O(n/ε²) oracle complexity for approximate submodular function minimization, down from ~O(n^{3/2}/ε²), with extensions to continuous submodular functions.
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Near-optimal Approximate Discrete and Continuous Submodular Function Minimization
A data-structure trick based on binary segment decomposition yields near-optimal ~O(n/ε²) oracle complexity for approximate submodular function minimization, down from ~O(n^{3/2}/ε²), with extensions to continuous submodular functions.