Sentence examples for proving hardness from inspiring English sources

We address the problem of proving hardness results for (fully) dense problems, which has been neglected despite the fruitful effort put in upper bounds.

We prove hardness results for the problem, namely for general directed networks we prove that it is NP-hard to find a Clogn-approximation, where C is a positive constant and n is the number of nodes of the network.

In this work, we prove hardness results of dense instances of a broad family of CSP problems, as well as a broad family of ranking problems which we refer to as CSP-Rank.

Our techniques involve a construction of a pseudorandom hypergraph coloring, which generalizes the well-known Paley graph, recently used by Alon to prove hardness of feedback arc-set in tournaments.

Before proving the hardness, we make the following observation that follows from a simple local improvement argument.

This technique is very efficient in proving NP-hardness of the existence of a Nash equilibrium.

They also proved a hardness result indicating it is NP-hard to approximate the problem within a factor of O(r/logr).

Moreover, we give an explanation of what makes a problem hard to EAs, and based on the recognition, we prove the hardness of a general problem.

They proved NP hardness of the problem and linearized it in three different ways.

In the later set of samples, was possible to prove that hardness is proportional to the ion current density.

This paper addresses the problem of finding an optimal ordering, proves its hardness, and gives several heuristics for finding an optimal ordering in the distributed environment.