A Fully Polynomial Time Approximation Scheme For A NP-Hard Problem

07/02/2020

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by   Marius-Simion Costandin, et al.

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We present a novel feasibility criteria for the intersection of convex sets given by inequalities. This criteria allows us to easily assert the feasibility by analyzing the unconstrained minimum of a certain convex function, that we form with the given sets. Next an algorithm is presented which extends the idea to a particular non-convex case: assert the inclusion of the intersection of a set of balls with equal radii in another ball with a different radius. Given a certain condition on the radii is met, our method can decide if the inclusion happens or not. The condition on the radii can be seen as a generalization of linear programming. Next we apply the results to approximate the solution of a NP-hard problem.