On the Travelling Salesperson Problem in Many Dimensions

Consider d ? 2, and m points X₁, …, X_m that are independent uniformly distributed in 0, 1]^d. It is well known that the length T_m of the shortest tour through X₁, …, X_m satisfies lim_m→∞ E(T_m)/m^1?1/d = β(d) for a certain number β(d). We show that for some numerical constant K, .