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arXiv · 2110.09901

A FPTAS for the Subset Sum Problem with Real Numbers

Marius Costandin
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Abstract

In this paper we study the subset sum problem with real numbers. Starting from the given problem, we formulate a quadratic maximization problem over a polytope which is eventually written as a distance maximization to a fixed point. For solving this, we provide a polynomial algorithm which maximizes the distance to a fixed point over a certain convex set. This convex set is obtained by intersecting the unit hypercube with two relevant half spaces. We show that in case the subset sum problem has a solution, our algorithm gives the correct maximum distance up to an arbitrary chosen precision. In such a case, we show that the obtained maximizer is a solution to the subset sum problem. Therefore, we compute the maximizer and upon analyzing it we can assert the feasibility of the subset sum problem.

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Marius Costandin. 2021-10-17. A FPTAS for the Subset Sum Problem with Real Numbers. https://arxiv.org/abs/2110.09901

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