论文标题
一种新颖有效的算法来解决子集总和问题
A novel and efficient algorithm to solve subset sum problem
论文作者
论文摘要
在本文中，我们建议分析方法和相关算法来确定集合$ x_n $的子集$ x_m $（子集总和问题）。 Our algorithm has time complexity $T=O(C_{n}^{k})$ ($k=[m/2]$, which significantly improves upon all known algorithms. This algorithm is applicable to all NP-complete problems. Moreover, the algorithm has memory complexity $M=O(C_n^k)$, which makes our algorithm applicable to real-world problems. At首先，我们如何将算法用于小尺寸$ M = 4、5、6、7、8 $，我们建立了$ m> 8 $的一般方法结果，它打开了一种证明$ p $与NP问题（七千年奖品问题之一）的方法。
In this paper we suggest analytical methods and associated algorithms for determining the sum of the subsets $X_m$ of the set $X_n$ (subset sum problem). Our algorithm has time complexity $T=O(C_{n}^{k})$ ($k=[m/2]$, which significantly improves upon all known algorithms. This algorithm is applicable to all NP-complete problems. Moreover, the algorithm has memory complexity $M=O(C_n^k)$, which makes our algorithm applicable to real-world problems. At first, we show how to use the algorithm for small dimensions $m=4 ,5 ,6 ,7 ,8$. After that we establish a general methodology for $m>8$. The main idea is to split the original set $X_n$ (the algorithm becomes even faster with sorted sets) into smaller subsets and use parallel computing. This approach might be a significant breakthrough towards finding an efficient solution to $NP$-complete problems. As a result, it opens a way to prove the $P$ versus NP problem (one of the seven Millennium Prize Problems).
