How hard is it to invert NP-problems? We show that all superlinearly certified inverses of NP problems are coNP-hard. To do so, we develop a novel proof technique that builds diagonalizations against certificates directly into a circuit.

How hard is it to invert NP-problems? We show that all superlinearly certified inverses of NP problems are coNP-hard. To do so, we develop a novel proof technique that builds diagonalizations against certificates directly into a circuit.

Recall that the approximation ratio for an approximation algorithm is a measure to evaluate the approximation performance of the algorithm. The closer the ratio to 1 the better the approximation performance of the algorithm. It is notable that there is a class of NP-hard optimization problems, most originating from scheduling problems, for which there are polynomial time approximation algorithm...

The vertex cover problem Find a set of vertices that cover the graph LP rounding is a 4 step scheme to approximate combinatorial problems with theoretical guarantees on solution quality. Several problems in machine learning, computer vision and data analysis can be formulated using NP-­‐hard combinatorial optimization problems. In many of these applications, approximate solutions for these NP-­...

Cook's Theorem [Cormen, T.H., Leiserson, C.E., Rivest, R.L., 2001. Introduction to Algorithms, second ed., The MIT Press; Garey, M.R., Johnson, D.S., 1979. Computer and Intractability, Freeman, San Fransico, CA] is that if one algorithm for an NP-complete or an NP-hard problem will be developed, then other problems will be solved by means of reduction to that problem. Cook's Theorem has been de...

The theory of NP-completeness, as developed by Cook, Levin, and Karp, states that any language, L in NP is reducible to the Boolean satisfiability problem, 3SAT. By this, we mean that for every instance, x of the language L, we can obtain a satisfiability instance, φ such that x ∈ L if and only if φ is satisfiable. Thus, 3SAT is at least as hard as any other problem in NP. Karp further showed t...