  In this paper, we consider a problem of covering a straight line segment by
equal circles that are initially arbitrarily placed on a plane by moving their
centers on a segment or on a straight line containing a segment so that the
segment is completely covered, the neighboring circles in the cover are
touching each other and the total length of the paths traveled by circles is
minimal. The complexity status of the problem is not known. We propose a
$O(n^{2+c}/\varepsilon^2)$--time FPTAS for this problem, where $n$ is the
number of circles and $c>0$ is arbitrarily small real.
