Submodular function minimization has gained a lot of interest in recent years. They are highly applicable in the area of Computer Vision and Machine Learning. Often such applications require to work with submodular functions defined on distributive lattice. Current best way of dealing with it is using a transformation which extrapolates the submodular function for the respective boolean lattice. It makes optimization system too inefficient due to enlargement of the working space. Quantitatively, the expanded space has additional exponential (in set size) number of elements. We propose a generic framework for dealing with distributive lattice which only works within distributive lattice. Our framework allows one to use already established submodular function minimization algorithms for boolean lattice. In our experiment, we show the huge improvement in terms of running time over tranditional methods for handling distributive lattice.

翻译：次模函数最小化近年来引起了广泛关注，在计算机视觉和机器学习领域具有高度适用性。这类应用通常需要处理定义在分配格上的次模函数。目前处理该问题的最佳方式是通过一种转换方法，将次模函数外推到相应的布尔格上。然而，由于工作空间的扩大，这种转换使得优化系统效率过低。从定量角度看，扩展后的空间包含额外呈指数级（相对于集合大小）增长的元素数量。我们提出了一种仅在分配格内运行的通用框架，用于处理分配格问题。该框架允许直接使用已建立的布尔格次模函数最小化算法。实验表明，在处理分配格时，我们的方法相较于传统方法在运行时间上实现了显著提升。