In this paper the authors propose a novel geometry based algorithm for maximizing the distance to a point over an intersection of balls. Some novel results the area are developed. The results are then applied to the Subset Sum Problem (SSP). Given a SSP it is shown that it has a solution iff a distance maximization over an intersection of balls to a fixed given point has a predefined value. Then, under the assumption that the SSP has at most one solution, using the derived results regarding the maximization of distances over intersection of balls, a characterization of the unique solution to the SSP is made.

翻译：本文作者提出了一种新颖的基于几何的算法，用于在球交集中最大化到某点的距离。文中发展了该领域的一些创新性成果，并将这些成果应用于子集和问题（SSP）。针对给定的SSP，研究表明其有解当且仅当在球交集中到固定点的距离最大化问题存在一个预定义值。进而，在假设SSP至多存在一个解的条件下，利用所推导的关于球交集中距离最大化的结果，给出了SSP唯一解的表征。