Mohs scale of mineral hardness Mohs scale of mineral hardness The Mohs scale of mineral hardness is a qualitative ordinal scale characterizing scratch resistance of various minerals through the ability of harder material to scratch softer material. Created in 1812 by German geologist and mineralogist Friedrich Mohs, it is one of several definitions of hardness in materials science, some of which are more quantitative. The method of comparing hardness by seeing which minerals can visibly scratch others is, however, of great antiquity, having been mentioned by Theophrastus in his treatise "On Stones", c. 300 BC, followed by Pliny the Elder in his "Naturalis Historia", c.
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