中文摘要：

几乎所有子集与密度加问题，是众所周知的不到 0.9408 吗？？能与能在一个特殊格子发现最短的向量的 SVP 神谕在多项式时间被解决。在这份报纸，作者证明类似的结果为与一模一样的答案有 k 子集和问题的 k 多重的子集和问题成立。特殊，为单个子集加问题(k = 1 ) ，一个修改格子被介绍为比以前紧密的成功概率使建议分析成为更简单的大部分和界限。而且，多重子集和问题的一些扩大版本也被考虑。

英文摘要：

It is well known that almost all subset sum problems with density less than 0.9408… can be solved in polynomial time with an SVP oracle that can find a shortest vector in a special lattice.In this paper,the authors show that a similar result holds for the k-multiple subset sum problem which has k subset sum problems with exactly the same solution.Specially,for the single subset sum problem（k=1）,a modified lattice is introduced to make the proposed analysis much simpler and the bound for the success probability tighter than before.Moreover,some extended versions of the multiple subset sum problem are also considered.