Computer Science – Data Structures and Algorithms
Scientific paper
2008-02-20
Dans Proceedings of the 25th Annual Symposium on the Theoretical Aspects of Computer Science - STACS 2008, Bordeaux : France (
Computer Science
Data Structures and Algorithms
Scientific paper
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 $k$ sets from $\scr F$ in time within a polynomial factor (in $n$) of the number of supersets of the members of $\scr F$. Relying on an intersection theorem of Chung et al. (1986) to bound the sizes of set families, we apply these ideas to well-studied combinatorial optimisation problems on graphs of maximum degree $\Delta$. In particular, we show how to compute the Domatic Number in time within a polynomial factor of $(2^{\Delta+1-2)^{n/(\Delta+1)$ and the Chromatic Number in time within a polynomial factor of $(2^{\Delta+1-\Delta-1)^{n/(\Delta+1)$. For any constant $\Delta$, these bounds are $O\bigl((2-\epsilon)^n\bigr)$ for $\epsilon>0$ independent of the number of vertices $n$.
Björklund Andreas
Husfeldt Thore
Kaski Petteri
Koivisto Mikko
No associations
LandOfFree
Trimmed Moebius Inversion and Graphs of Bounded Degree does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Trimmed Moebius Inversion and Graphs of Bounded Degree, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Trimmed Moebius Inversion and Graphs of Bounded Degree will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-647782