Complex sentence: Although the approximation ratio of this algorithm is weak, it is the best known to date, and the results on hardness of approximation described below suggest that there can be no approximation algorithm with an approximation ratio significantly less than linear.
Split into simpler sentences: Although the approximation ratio of this algorithm is weak, it is the best known to date. The results on hardness of approximation described below suggest that there can be no approximation algorithm with an approximation ratio significantly less than linear.