  We study the minimum diameter problem for a set of inexact points. By
inexact, we mean that the precise location of the points is not known. Instead,
the location of each point is restricted to a contineus region ($\impre$ model)
or a finite set of points ($\indec$ model). Given a set of inexact points in
one of $\impre$ or $\indec$ models, we wish to provide a lower-bound on the
diameter of the real points.
  In the first part of the paper, we focus on $\indec$ model. We present an
$O(2^{\frac{1}{\epsilon^d}} \cdot \epsilon^{-2d} \cdot n^3 )$ time
approximation algorithm of factor $(1+\epsilon)$ for finding minimum diameter
of a set of points in $d$ dimensions. This improves the previously proposed
algorithms for this problem substantially.
  Next, we consider the problem in $\impre$ model. In $d$-dimensional space, we
propose a polynomial time $\sqrt{d}$-approximation algorithm. In addition, for
$d=2$, we define the notion of $\alpha$-separability and use our algorithm for
$\indec$ model to obtain $(1+\epsilon)$-approximation algorithm for a set of
$\alpha$-separable regions in time $O(2^{\frac{1}{\epsilon^2}}\allowbreak .
\frac{n^3}{\epsilon^{10} .\sin(\alpha/2)^3} )$.
