Separating sublinear time computations by approximate diameter

We study sublinear time complexity and algorithm to approximate the diameter for a sequence S = p(1)p(2)... p(n) of points in a metric space, in which every pair of two consecutive point's p(i) and p(i+i) in the sequence S has the same distance. The diameter of S is the largest distance between two points p(i) and p(j) in S. The approximate diameter problem is investigated under deterministic, zero error randomized, and bounded error randomized models. We obtain a class of separations about the sublinear time computations using various versions of the approximate diameter problem based on the restriction about, the format of input data.