  Prune-and-search is an important paradigm for solving many important
geometric problems. We show that the general prune-and-search technique can be
implemented where the objects are given in read-only memory. As examples we
consider convex-hull in 2D, and linear programming in 2D and 3D. For the
convex-hull problem, designing sub-quadratic algorithm in a read-only setup
with sub-linear space is an open problem for a long time. We first propose a
simple algorithm for this problem that runs in $O(n^{3/2+\epsilon)}$ time and
$O(n^(1/2))$ space. Next, we consider a restricted version of the problem where
the points in $P$ are given in sorted order with respect to their
$x$-coordinates in a read-only array. For the linear programming problems, the
constraints are given in the read-only array. The last three algorithms use
{\it prune-and-search}, and their time and extra work-space complexities are
$O(n^{1 + \epsilon})$ and $O(\log n)$ respectively, where $\epsilon$ is a small
constant satisfying $\sqrt{\frac{\log\log n}{\log n}} < \epsilon < 1$.
