Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: Submodular functions describe a variety of discrete problems in machine learn-<lb>ing, signal processing, and computer vision. However, minimizing submodular<lb>functions poses a number of algorithmic challenges. Recent work introduced an<lb>easy-to-use, parallelizable algorithm for minimizing submodular functions that<lb>decompose as the sum of “simple” submodular functions. Empirically, this al-<lb>gorithm performs extremely well, but no theoretical analysis was given. In this<lb>paper, we show that the algorithm converges linearly, and we provide upper and<lb>lower bounds on the rate of convergence. Our proof relies on the geometry of<lb>submodular polyhedra and draws on results from spectral graph theory.

On the Convergence Rate of Decomposable Submodular Function Minimization