SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On Constrained Hypergraph Coloring and Scheduling
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Random Structures & Algorithms
An algorithmic Friedman--Pippenger theorem on tree embeddings and applications to routing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Conflict-free colourings of graphs and hypergraphs
Combinatorics, Probability and Computing
The lovász-local-lemma and scheduling
Efficient Approximation and Online Algorithms
Constraint satisfaction, packet routing, and the lovasz local lemma
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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The Lovász local lemma (LLL) is a powerful tool that is increasingly playing a valuable role in computer science. The original lemma was nonconstructive; a breakthrough of Beck and its generalizations (due to Alon and Molloy and Reed) have led to constructive versions. However, these methods do not capture some classes of applications of the LLL. We make progress on this by providing algorithmic approaches to two families of applications of the LLL. The first provides constructive versions of certain applications of an extension of the LLL (modeling, e.g., hypergraph-partitioning and low-congestion routing problems); the second provides new algorithmic results on constructing disjoint paths in graphs. Our results can also be seen as constructive upper bounds on the integrality gap of certain packing problems. One common theme of our work is a "gradual rounding" approach.