On molecular approximation algorithms for NP optimization problem

We develop a general technique for constructing molecular-based approximation algorithms for NP optimization problems. Our algorithms exhibit a useful volume{ accuracy tradeoo. In particular we solve the Covering problem of Hochbaum and Maass using polynomial time and O ` 2 (log`)n 2 ? n(n?1) ` 2 =2 volume with error ratio (1 + 1 `) 2. We also present the rst candidate for a problem that can be solved more eeciently with the Amplify operation than without.