Improved hardness amplification in NP

Uniform Hardness Amplification in NP via Monotone Codes

We consider the problem of amplifying uniform average-case hardness of languages in NP, where hardness is with respect to BPP algorithms. We introduce the notion of monotone errorcorrecting codes, and show that hardness amplification for NP is essentially equivalent to constructing efficiently locally encodable and locally list-decodable monotone codes. The previous hardness amplification resul...

Hardness Ampli ation Within NP

NP-Hardness of Cache Mapping

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NP-hardness of sortedness constraints

In Constraint Programming, global constraints allow to model and solve many combinatorial problems. Among these constraints, several sortedness constraints have been defined, for which propagation algorithms are available, but for which the tractability is not settled. We show that the sort(U, V ) constraint (Older et. al, 1995) is intractable (assuming P 6=NP) for integer variables whose domai...

On Percolation and NP-Hardness

We consider the robustness of computational hardness of problems whose input is obtained by applying independent random deletions to worst-case instances. For some classical NPhard problems on graphs, such as Coloring, Vertex-Cover, and Hamiltonicity, we examine the complexity of these problems when edges (or vertices) of an arbitrary graph are deleted independently with probability 1−p > 0. We...