Robust Satisfiability for CSPs

Víctor Dalmau, Andrei Krokhin
2013 ACM Transactions on Computation Theory  
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more » ... full DRO policy for further details. An algorithm for a constraint satisfaction problem is called robust if it outputs an assignment satisfying at least a (1−f (ϵ))-fraction of constraints for each (1−ϵ)-satisfiable instance (i.e. such that at most a ϵ-fraction of constraints needs to be removed to make the instance satisfiable), where f (ϵ) → 0 as ϵ → 0. We establish an algebraic framework for analyzing constraint satisfaction problems admitting an efficient robust algorithm with functions f of a given growth rate. We use this framework to derive hardness results. We also describe three classes of problems admitting an efficient robust algorithm such that f is O(1/ log (1/ϵ)), O(ϵ 1/k ) for some k > 1, and O(ϵ), respectively. Finally, we give a complete classification of robust satisfiability with a given f for the Boolean case.
doi:10.1145/2540090 fatcat:25oavt5iyrfebaf5iyngqzadxu