  We consider the k-strong conflict-free coloring of a set of points on a line
with respect to a family of intervals: Each point on the line must be assigned
a color so that the coloring has to be conflict-free, in the sense that in
every interval I there are at least k colors each appearing exactly once in I.
In this paper, we present a polynomial algorithm for the general problem; the
algorithm has an approximation factor 5-2/k when k\geq2 and approximation
factor 2 for k=1. In the special case the family contains all the possible
intervals on the given set of points, we show that a 2 approximation algorithm
exists, for any k\geq1.
