For a given set S of nonnegative integers the partitioning problem asks for a partition of S into two disjoint subsets S1 and S2 such that the sum of elements in S1 is equal to the sum of elements in S2. If additionally two elements (the kernels) r1, r2 ∈ S are given which must not be assigned to the same set Si, we get the partitioning problem with kernels. For these NP-complete problems the authors present two compound algorithms which consist both of three linear greedylike algorithms running independently. It is shown that the worst-case performance of the heuristic for the ordinary partitioning problem is 12/11, while the second procedure for partitioning with kernels has a bound of 8/7.
