  Suppose that in a given planar circular region, there are some smart mobile
evaders and we would like to find them using sweeping agents. We assume that
the sweeping agents are in a line formation whose total length is 2r. We
propose procedures for designing a sweeping process that ensures the successful
completion of the task, thereby deriving conditions on the sweeping velocity of
the linear formation and its path. Successful completion of the task means that
evaders with a given limit on their velocity cannot escape the sweeping agents.
A simpler task for the sweeping formation is the confinement of the evaders to
their initial domain. The feasibility of completing these tasks depends on
geometric and dynamic constraints that impose a lower bound on the velocity
that the sweeper line formation must have. This critical velocity is derived to
ensure the satisfaction of the confinement task. Increasing the velocity above
the lower bound enables the agents to complete the search task as well. We
present results on the total search time as a function of the sweeping velocity
of the formation given the initial conditions on the size of the search region
and the maximal velocity of the evaders.
