Scratch hardness Scratch hardness Scratch hardness tests are used to determine the hardness of a material to scratches and abrasion. The earliest test was developed by mineralogist Friedrich Mohs in 1820 (see Mohs scale). It is based on relative scratch hardness, with talc assigned a value of 1 and diamond assigned a value of 10. Mohs' scale had two limitations; it was not linear, and most modern abrasives fall between 9 and 10. Raymond R. Ridgway, a research engineer at the Norton Company, modified the Mohs scale by giving garnet a hardness of 10 and diamond a hardness of 15. Charles E.
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