  In this paper, we study the online class cover problem where a (finite or
infinite) family $\cal F$ of geometric objects and a set ${\cal P}_r$ of red
points in $\mathbb{R}^d$ are given a prior, and blue points from $\mathbb{R}^d$
arrives one after another. Upon the arrival of a blue point, the online
algorithm must make an irreversible decision to cover it with objects from
$\cal F$ that do not cover any points of ${\cal P}_r$. The objective of the
problem is to place a minimum number of objects. When $\cal F$ consists of
axis-parallel unit squares in $\mathbb{R}^2$, we prove that the competitive
ratio of any deterministic online algorithm is $\Omega(\log |{\cal P}_r|)$, and
also propose an $O(\log |{\cal P}_r|)$-competitive deterministic algorithm for
the problem.
