  In this paper, we focus on lower bounds and algorithms for some basic
geometric problems in the one-pass (insertion only) streaming model. The
problems considered are grouped into three categories:
  (i) Klee's measure
  (ii) Convex body approximation, geometric query, and
  (iii) Discrepancy
  Klee's measure is the problem of finding the area of the union of
hyperrectangles. Under convex body approximation, we consider the problems of
convex hull, convex body approximation, linear programming in fixed dimensions.
The results for convex body approximation implies a property testing type
result to find if a query point lies inside a convex polyhedron. Under
discrepancy, we consider both the geometric and combinatorial discrepancy. For
all the problems considered, we present (randomized) lower bounds on space.
Most of our lower bounds are in terms of approximating the solution with
respect to an error parameter $\epsilon$. We provide approximation algorithms
that closely match the lower bound on space for most of the problems.
