Sentence examples for prove hardness from inspiring English sources
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.
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.
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.
We address the problem of proving hardness results for (fully) dense problems, which has been neglected despite the fruitful effort put in upper bounds.
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.
In the later set of samples, was possible to prove that hardness is proportional to the ion current density.
They also proved a hardness result indicating it is NP-hard to approximate the problem within a factor of O(r/logr).
They proved NP hardness of the problem and linearized it in three different ways.
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.
Fragmentation of samples B and C was more severe than that of sample A. The nanoindentation and particle strength tests proved that hardness and mechanical strength are the dominant factors of attrition resistances.
In particular, we study the problem of adding a minimum size set of points to a given unit disk graph in such a way that in the resulting graph any two original points have hop-distance at most a given bound D. After having proved the hardness of the problem, we propose two different bi-criteria algorithms that, conjunctively, provide logarithmic approximation ratio on both criteria.
