Constraint satisfaction, packet routing, and the lovasz local lemma

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.

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