Submodular Function Minimization

This lecture covers the concept of submodular functions and their minimization, defining submodularity as f(A) + f(B) >= f(AUB) + f(AMB) for all A, B subsets of the ground set N. It also explains the intuition behind submodularity, focusing on diminishing returns. Examples of submodular functions, such as graph cut functions, are provided to illustrate the concept. The instructor discusses the Lovász Extension and its role in submodular function minimization, emphasizing the uniformity of the extension. The lecture concludes with the application of submodular functions in influence maximization, where the goal is to select a set of individuals to maximize the spread of influence in a network.