Global Optimal Trajectory in Chaos and NP-Hardness

Nearly Optimal NP-Hardness of Unique Coverage

The Unique Coverage problem, given a universe V of elements and a collection E of subsets of V , asks to find S ⊆V to maximize the number of e ∈ E that intersects S in exactly one element. When each e ∈ E has cardinality at most k, it is also known as 1-in-k Hitting Set, and admits a simple Ω( 1 logk )-approximation algorithm. For constant k, we prove that 1-in-k Hitting Set is NP-hard to appro...

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...

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...