  Consider a given planar circular region, in which there is an unknown number
of smart mobile evaders. We wish to detect evaders using a line formation of
sweeping agents whose total sensing length is predetermined. We propose
procedures for designing spiral sweeping protocols that ensure the successful
completion of the task, thus deriving conditions on the sweeping speed of the
linear formation and its path. Successful completion of the task implies that
evaders with a given limit on their speed cannot escape the sweeping agents. A
simpler task for the sweeping formation is the confinement of evaders to a
desired region, such as their original domain. The feasibility of completing
these tasks depends on geometric and dynamic constraints that impose a lower
bound on the speed that the sweeping agents must have. This critical speed is
derived to ensure the satisfaction of the confinement task. Increasing the
speed above the lower bound enables the sweepers to complete the search task as
well. We develop two spiral line formation search processes for smart evaders,
that address current limitations in search against smart evaders. Additionally,
we present a quantitative and qualitative comparison analysis between the total
search time of circular line formation sweep processes and spiral line
formation processes. We evaluate the different strategies by using two metrics,
total search time and the minimal critical speed required for a successful
search.
