  We study the problem of planning the deployments of a group of mobile robots.
While the problem and formulation can be used for many different problems, here
we use a bridge inspection as the motivating application for the purpose of
exposition. The robots are initially stationed at a set of depots placed
throughout the bridge. Each robot is then assigned a set of sites on the bridge
to inspect and, upon completion, must return to the same depot where it is
stored.
  The problem of robot planning is formulated as a rooted min-max cycle cover
problem, in which the vertex set consists of the sites to be inspected and
robot depots, and the weight of an edge captures either (i) the amount of time
needed to travel from one end vertex to the other vertex or (ii) the necessary
energy expenditure for the travel. In the first case, the objective function is
the total inspection time, whereas in the latter case, it is the maximum energy
expenditure among all deployed robots. We propose a novel algorithm with
approximation ratio of $5 + \epsilon$, where $0<\epsilon<1$. In addition, the
computational complexity of the proposed algorithm is shown to be $O\big(
n^2+2^{m-1} n \log(n+k) \big)$, where $n$ is the number of vertices, and $m$ is
the number of depots.
