Inapproximability Results
Lund & Yannakakis (1994) showed that set covering cannot be approximated in polynomial time to within a factor of, unless NP has quasi-polynomial time algorithms. Feige (1998) improved this lower bound to under the same assumptions, which essentially matches the approximation ratio achieved by the greedy algorithm. Raz & Safra (1997) established a lower bound of, where is a constant, under the weaker assumption that PNP. A similar result with a higher value of was recently proved by Alon, Moshkovitz & Safra (2006).
Read more about this topic: Set Cover Problem
Famous quotes containing the word results:
“It would be easy ... to regard the whole of world 3 as timeless, as Plato suggested of his world of Forms or Ideas.... I propose a different viewone which, I have found, is surprisingly fruitful. I regard world 3 as being essentially the product of the human mind.... More precisely, I regard the world 3 of problems, theories, and critical arguments as one of the results of the evolution of human language, and as acting back on this evolution.”
—Karl Popper (19021994)