A FPTAS for the Subset Sum Problem with Real Numbers
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.
Cite
@article{arxiv.2110.09901,
title = {A FPTAS for the Subset Sum Problem with Real Numbers},
author = {Marius Costandin},
journal= {arXiv preprint arXiv:2110.09901},
year = {2023}
}
Comments
It relies on maximizing the distance over an intersection of balls to a given point. The used algorithm for this however, is not able to solve the class of problem the SSP generates