  We consider the discrepancy problem of coloring $n$ intervals with $k$ colors
such that at each point on the line, the maximal difference between the number
of intervals of any two colors is minimal. Somewhat surprisingly, a coloring
with maximal difference at most one always exists. Furthermore, we give an
algorithm with running time $O(n \log n + kn \log k)$ for its construction.
This is in particular interesting because many known results for discrepancy
problems are non-constructive. This problem naturally models a load balancing
scenario, where $n$ tasks with given start- and endtimes have to be distributed
among $k$ servers. Our results imply that this can be done ideally balanced.
  When generalizing to $d$-dimensional boxes (instead of intervals), a solution
with difference at most one is not always possible. We show that for any $d \ge
2$ and any $k \ge 2$ it is NP-complete to decide if such a solution exists,
which implies also NP-hardness of the respective minimization problem.
  In an online scenario, where intervals arrive over time and the color has to
be decided upon arrival, the maximal difference in the size of color classes
can become arbitrarily high for any online algorithm.
