A Geometric Algorithm for Maximizing the Distance over an Intersection of Balls to a Given Point

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.