Subset Sum in O(n^16log(n))

03/20/2022

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by   Rion Tolchin, et al.

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This extensive revision of my paper "Description of an O(poly(n)) Algorithm for NP-Complete Combinatorial Problems" will dramatically simplify the content of the original paper by solving subset-sum instead of 3-SAT. I will first define the "product-derivative" method which will be used to generate a system of equations for solving unknown polynomial coefficients. Then I will describe the "Dragonfly" algorithm usable to solve subset-sum in O(n^16log(n)) which is itself composed of a set of symbolic algebra steps on monic polynomials to convert a subset, S_T, of a set of positive integers, S, with a given target sum, T into a polynomial with roots corresponding to the elements of S_T.