We investigate three kinds of optimization problems regarding n points in the 2-dimensional
plane that need to be enclosed by squares.(1) Find a given number of squares that enclose
all the points, minimizing the size of the largest square used.(2) Problem (1) with the
additional condition that the center of each enclosing square must lie on one of the two
given axis-parallel lines, which are either parallel or perpendicular.(3) Enclose the maximum
number of points, using a specified number of squares of a fixed size. We propose different …

We investigate two kinds of optimization problems regarding points in the 2-dimensional
plane that need to be enclosed by squares.(1) Given a set of n points, find a given number of
squares that enclose all the points, minimizing the size of the largest square used.(2) Given
a set of n points, enclose the maximum number of points, using a specified number of
squares of a fixed size. We provide different techniques to solve the above problems in
cases where squares are axis-parallel or of arbitrary orientation, disjoint or overlapping. All …