Trimmed Moebius Inversion and Graphs of Bounded Degree

Andreas BjöRklund, Thore Husfeldt, Petteri Kaski & Mikko Koivisto
We study ways to expedite Yates's algorithm for computing the zeta and Moebius transforms of a function defined on the subset lattice. We develop a trimmed variant of Moebius inversion that proceeds point by point, finishing the calculation at a subset before considering its supersets. For an $n$-element universe $U$ and a family $scr F$ of its subsets, trimmed Moebius inversion allows us to compute the number of packings, coverings, and partitions of $U$ with...