论文标题
凹面函数的凹面方面
Concave Aspects of Submodular Functions
论文作者
论文摘要
下函数是一类特殊的集合功能，它概括了几个信息理论数量，例如熵和互信息[1]。下函数具有亚级别和亚分化[2]，并允许最小化的多项式时间算法，这两种算法都是凸函数的基本特征。下函数还显示出类似于凹的符号。虽然NP-硬化虽然可以保证恒定因素近似，但肌函数的最大化虽然可以保证，并且由模块化函数组成的凹形功能是子模块的。在本文中，我们尝试提供更完整的描述与凹陷之间的关系之间的关系。我们表征了与上边界相关的超差异和多面体，并提供了使用superper差异的最大化条件。本文是我们更长的预印本[3]的简洁版本。
Submodular Functions are a special class of set functions, which generalize several information-theoretic quantities such as entropy and mutual information [1]. Submodular functions have subgradients and subdifferentials [2] and admit polynomial-time algorithms for minimization, both of which are fundamental characteristics of convex functions. Submodular functions also show signs similar to concavity. Submodular function maximization, though NP-hard, admits constant-factor approximation guarantees, and concave functions composed with modular functions are submodular. In this paper, we try to provide a more complete picture of the relationship between submodularity with concavity. We characterize the super-differentials and polyhedra associated with upper bounds and provide optimality conditions for submodular maximization using the-super differentials. This paper is a concise and shorter version of our longer preprint [3].
