考虑了限制性的带核元划分问题,即将一个整数集合划分为2个子集,使得2个核元分别在不同的子集里且每个子集至多包含k个元素,这里n/2+1≤后≤n+1,目标使2个子集中元素之和的最小者达尽可能大.对一般的k,给出了全多项式时问近似方案(FPTAS).当k=/2+1时,给出了线性时间内的多项式时间近似方案(PTAS)和全多项式时间近似方案(FPTAS).
The constrained partition problem with kernels is considered, which is to find a partition of the set S into two disjoint subsets under the two constraints that two kernels belong to different subsets and eachsubset contains at most k elements, here n/2 + 1 ~〈k ~〈 n + 1. The objective is to maximize the minimum sum of elements in each of the two subsets. An full polynomial - time approximation scheme (FPTAS) is designed for the general k. For the special version where k = n + 1, a polynomial -time approximation scheme (PTAS) and an full polynomial- time approximation scheme (FPTAS) with running times O(n) are designed.