 A naive algorithm of finding distances between all pairs of points in a space of dimension "d" and selecting the minimum requires time.It turns out that the problem may be solved in time in a Euclidean space or Lp space of fixed dimension d. In the algebraic decision tree model of computation, the algorithm is optimal, by a reduction from the element uniqueness problem.In the computational model that assumes that the floor function is computable in constant time the problem can be solved in time.