Approximation Results for Kinetic Variants of TSP

   Abstract. We study the approximation complexity of certain kinetic variants of the Traveling Salesman Problem (TSP) where we consider instances in which each point moves with a fixed constant speed in a fixed direction. We prove the following results: • If the points all move with the same velocity, then there is a polynomial time approximation scheme for the Kinetic TSP. • The Kinetic TSP cannot be approximated better than by a factor of 2 by a polynomial time algorithm unless P = NP, even if there are only two moving points in the instance. • The Kinetic TSP cannot be approximated better than by a factor of

A new free recoverable and reusable mono-alkaloid-type ligand and its use in preparation of ethyl （2R,3S）-2,3-dihydroxy-3-phenylpropionate

A new free recoverable and reusable mono-alkaloid-type ligand has been synthesized by a simple method.With highly polar groups,the ligand can be recycled and reused eight times to prepare ethyl(2R,3S)-2,3-dihydroxy-3-phenylpropionate with high yield and ee via asymmetric dihydroxylation(AD) reaction.