Further algorithmic aspects of the local lemma
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Improved bounds and algorithms for hypergraph 2-coloring
Random Structures & Algorithms
Coloring nonuniform hypergraphs: a new algorithmic approach to the general Lovász local lemma
Proceedings of the ninth international conference on on Random structures and algorithms
Efficient proper 2-coloring of almost disjoint hypergraphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating the Domatic Number
SIAM Journal on Computing
Distributions on Level-Sets with Applications to Approximation Algorithms
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Random Structures & Algorithms
Dependent rounding and its applications to approximation algorithms
Journal of the ACM (JACM)
Properly 2-Colouring Linear Hypergraphs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Asymptotically optimal frugal colouring
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A constructive proof of the Lovász local lemma
Proceedings of the forty-first annual ACM symposium on Theory of computing
A constructive proof of the general lovász local lemma
Journal of the ACM (JACM)
Asymptotically optimal frugal colouring
Journal of Combinatorial Theory Series B
Proceedings of the forty-second ACM symposium on Theory of computing
Deterministic algorithms for the Lovász Local Lemma
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the forty-third annual ACM symposium on Theory of computing
A kolmogorov complexity proof of the lovász local lemma for satisfiability
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
New Constructive Aspects of the Lovász Local Lemma
Journal of the ACM (JACM)
Survey: Randomly colouring graphs (a combinatorial view)
Computer Science Review
Journal of the ACM (JACM)
A Kolmogorov complexity proof of the Lovász Local Lemma for satisfiability
Theoretical Computer Science
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The Lovász Local Lemma is a powerful tool in combinatorics and computer science. The original version of the lemma was nonconstructive, and efficient algorithmic versions have been developed by Beck, Alon, Molloy & Reed, et al. In particular, the work of Molloy & Reed lets us automatically extract efficient versions of essentially any application of the symmetric version of the Local Lemma. However, with some exceptions, there is a significant gap between what one can prove using the original Lemma nonconstructively, and what is possible through these efficient versions; also, some of these algorithmic versions run in super-polynomial time. Here, we lessen this gap, and improve the running time of all these applications (which cover all applications in the Molloy & Reed framework) to polynomial. We also improve upon the parallel algorithmic version of the Local Lemma for hypergraph coloring due to Alon, by allowing noticeably more overlap among the edges.