Inclusion-exclusion algorithms for counting set partitions
Given a set U with n elements and a family of subsets S ⊆ 2U we show how to count the number of k-partitions S1 ∪ ... ∪ Sk = U into subsets Si ∈ S in time 2nnO(1). The only assumption on S is that it can be enumerated in time 2nnO(1). In effect we get exact algorithms in time 2nnO(1) for several well-studied partition problems including domatic number, chromatic number, bounded component spanning