Mohs scale of mineral hardness finding the hardest material that the given material can scratch, or the softest material that can scratch the given material. For example, if some material is scratched by apatite but not by fluorite, its hardness on the Mohs scale would fall between 4 and 5. "Scratching" a material for the purposes of the Mohs scale means creating non-elastic dislocations visible to the naked eye. Frequently, materials that are lower on the Mohs scale can create microscopic, non-elastic dislocations on materials that have a higher Mohs number. While these microscopic dislocations are permanent and sometimes detrimental to the harder material's structural
Hardness of approximation polynomial time. In the early 1990s, with the development of PCP theory, it became clear that many more approximation problems were hard to approximate, and that (unless P = NP) many known approximation algorithms achieved the best possible approximation ratio. Hardness of approximation theory deals with studying the approximation threshold of such problems. For an example of an NP-hard optimization problem that is hard to approximate, see set cover. Hardness of approximation In computer science, hardness of approximation is a field that studies the algorithmic complexity of finding near-optimal solutions to optimization problems. Hardness of approximation complements the study of