Combinatorica
A useful elementary correlation inequality
Journal of Combinatorial Theory Series A
Randomized Distributed Edge Coloring via an Extension of the Chernoff--Hoeffding Bounds
SIAM Journal on Computing
Split and balanced colorings of complete graphs
Discrete Mathematics
On the upper chromatic numbers of the reals
Discrete Mathematics
Universal Routing Strategies for Interconnection Networks
Universal Routing Strategies for Interconnection Networks
New Algorithmic Aspects of the Local Lemma with Applications to Routing and Partitioning
SIAM Journal on Computing
Constraint Satisfaction Problems and Finite Algebras
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Bounded size components: partitions and transversals
Journal of Combinatorial Theory Series B
A Note on Vertex List Colouring
Combinatorics, Probability and Computing
An Extension of the Lova´sz Local Lemma, and its Applications to Integer Programming
SIAM Journal on Computing
A constructive proof of the general lovász local lemma
Journal of the ACM (JACM)
Proceedings of the forty-third annual ACM symposium on Theory of computing
Universal packet routing with arbitrary bandwidths and transit times
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
New Constructive Aspects of the Lovász Local Lemma
Journal of the ACM (JACM)
The local lemma is tight for SAT
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A simpler proof for O(congestion+dilation) packet routing
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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Constraint-satisfaction problems (CSPs) form a basic family of NP-hard optimization problems that includes satisfiability. Motivated by the sufficient condition for the satisfiability of SAT formulae that is offered by the Lovasz Local Lemma, we seek such sufficient conditions for arbitrary CSPs. To this end, we identify a variable-covering radius--type parameter for the infeasible configurations of a given CSP, and also develop an extension of the Lovasz Local Lemma in which many of the events to be avoided have probabilities arbitrarily close to one; these lead to a general sufficient condition for the satisfiability of arbitrary CSPs. One primary application is to packet-routing in the classical Leighton-Maggs-Rao setting, where we introduce several additional ideas in order to prove the existence of near-optimal schedules; further applications in combinatorial optimization are also shown.