Guaiacum uses, including as lumber, for medicinal purposes, and as ornamentals. The trade of all species of "Guaiacum" is controlled under CITES Appendix II. "Guaiacum officinale" is the national flower of Jamaica, while "Guaiacum sanctum" is the national tree of the Bahamas. The genus is famous as the supplier of lignum vitae, which is the heartwood of several species in the genus. It is the fourth-hardest variety of wood as measured by the Janka hardness test, requiring a force of to embed a steel ball in diameter half that distance into the wood. The Spanish encountered guaiacum wood when they conquered
Hardness of approximation 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 approximation algorithms by proving, for certain problems, a limit on the factors with which their solution can be efficiently approximated. Typically such limits show a factor of approximation beyond which a problem becomes NP-hard, implying that finding a polynomial time approximation for the problem is impossible unless NP=P. Some hardness of approximation results, however, are based on other hypotheses, a notable one among which is the unique games conjecture.