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
Computational hardness assumption which is a computational hardness assumption about random instances of 3-SAT (sampled to maintain a specific ratio of clauses to variables). Average-case computational hardness assumptions are useful for proving average-case hardness in applications like statistics, where there is a natural distribution over inputs. Additionally, the planted clique hardness assumption has also been used to distinguish between polynomial and quasi-polynomial worst-case time complexity of other problems, similarly to the Exponential Time Hypothesis. The Unique Label Cover problem is a constraint satisfaction problem, where each constraint formula_60 involves two variables formula_77, and for each value of formula_26 there is a "unique" value