论文标题
子集总和$ O（n^{11} \ log（n））$
Subset Sum in $O(n^{11}\log(n))$
论文作者
论文摘要
本文描述了一种算法（迄今为止称为“蜻蜓算法”），可以在$ O（n^{11} \ log（n））$时复杂性中解决子集问题。本文将首先详细介绍广义的“产品衍生”方法（以及该方法的更有效的版本，该方法将在算法中使用），通过该方法，可以使用一对一元多项式来生成一个独特的一频性多项式系统，该系统将与该系统中的每种多项式都可以与其他奇异的植物相等，以与原始的奇异相互互动，以均匀的相对均配对。然后，该方法将应用于一对多项式上，其中一种$ ϕ（x）$是根据子集问题的实例展示已知的根，另一个$ t（x）$，其中包含未知的占位符系数，代表$ ϕ（x）$的线性子集的未知子集。
This paper describes an algorithm (thus far referred to as the "Dragonfly Algorithm") by which the subset-sum problem can be solved in $O(n^{11}\log(n))$ time complexity. The paper will first detail the generalized "product-derivative" method (and the more efficient version of this method which will be used in the algorithm) by which a pair of monic polynomials can be used to generate a system of unique monic polynomials for which each polynomial in the system will share with every other a set of roots equivalent to the intersection of the roots of the original pair; this method will then be applied on a pair of polynomials one of which, $ϕ(x)$, exhibiting known roots based on the instance of the subset-sum problem and the other of which, $t(x)$, containing unknown placeholder coefficients and representing an unknown subset of the linear factors of $ϕ(x)$.
