New Constructive Aspects of the Lovasz Local Lemma

Details New Constructive Aspects of the Lovasz Local Lemma New Constructive Aspects of the Lovasz Local Lemma

2010-01-08

arxiv.org/abs/1001.1231v5

Computer Science

Data Structures and Algorithms

23 pages

Scientific paper

The Lov\'{a}sz Local Lemma (LLL) states that the probability that none of a set of "bad" events happens is nonzero if the probability of each event is small compared to the number of bad events it depends on. A series of results have provided algorithms to efficiently construct structures whose existence is (non-constructively) guaranteed by the full asymmetric LLL, culminating in the recent breakthrough of Moser & Tardos. We show that the output distribution of the Moser-Tardos procedure has sufficient randomness, leading to two classes of algorithmic applications. We first show that when an LLL application provides a small amount of slack, the running time of the Moser-Tardos algorithm is polynomial in the number of underlying independent variables (not events!), and can thus be used to give efficient constructions in cases where the underlying proof applies the LLL to super-polynomially many events (or where finding a bad event that holds is computationally hard). We demonstrate our method on applications including: the first constant-factor approximation algorithm for the Santa Claus problem, as well as efficient algorithms for acyclic edge coloring, non-repetitive graph colorings, and Ramsey-type graphs. Second, we show applications to cases where a few of the bad events can hold, leading to the first such algorithmic applications of the LLL: MAX $k$-SAT is an illustrative example of this.

Affiliated with

Also associated with

No associations

Rating

New Constructive Aspects of the Lovasz Local Lemma 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 New Constructive Aspects of the Lovasz Local Lemma, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and New Constructive Aspects of the Lovasz Local Lemma will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-502112