Set partitioning via inclusion-exclusion
Given a set N with n elements and a family F of subsets, we show how to partition N into k such subsets in 2(n) n(O)(1) time. We also consider variations of this problem where the subsets may overlap or are weighted, and we solve the decision, counting, summation, and optimization versions of these problems. Our algorithms are based on the principle of inclusion-exclusion and the zeta transform. I
