  Classical separability problem involving multi-color point sets is an
important area of study in computational geometry. In this paper, we study
different separability problems for bichromatic point set P=P_r\cup P_b on a
plane, where $P_r$ and $P_b$ represent the set of n red points and m blue
points respectively, and the objective is to compute a monochromatic object of
the desired type and of maximum size. We propose in-place algorithms for
computing (i) an arbitrarily oriented monochromatic rectangle of maximum size
in R^2, (ii) an axis-parallel monochromatic cuboid of maximum size in R^3. The
time complexities of the algorithms for problems (i) and (ii) are
O(m(m+n)(m\sqrt{n}+m\log m+n \log n)) and O(m^3\sqrt{n}+m^2n\log n),
respectively. As a prerequisite, we propose an in-place construction of the
classic data structure the k-d tree, which was originally invented by J. L.
Bentley in 1975. Our in-place variant of the $k$-d tree for a set of n points
in R^k supports both orthogonal range reporting and counting query using O(1)
extra workspace, and these query time complexities are the same as the
classical complexities, i.e., O(n^{1-1/k}+\mu) and O(n^{1-1/k}), respectively,
where \mu is the output size of the reporting query. The construction time of
this data structure is O(n\log n). Both the construction and query algorithms
are non-recursive in nature that do not need O(\log n) size recursion stack
compared to the previously known construction algorithm for in-place k-d tree
and query in it. We believe that this result is of independent interest. We
also propose an algorithm for the problem of computing an arbitrarily oriented
rectangle of maximum weight among a point set P=P_r \cup P_b, where each point
in P_b (resp. P_r) is associated with a negative (resp. positive) real-valued
weight that runs in O(m^2(n+m)\log(n+m)) time using O(n) extra space.
