  We consider a perimeter defense problem in which a single vehicle seeks to
defend a compact region from intruders in a one-dimensional environment
parameterized by the perimeter size and the intruder-to-vehicle speed ratio.
The intruders move inward with fixed speed and direction to reach the
perimeter. We provide both positive and negative worst-case performance results
over the parameter space using competitive analysis. We first establish
fundamental limits by identifying the most difficult parameter combinations
that admit no $c$-competitive algorithms for any constant $c\geq 1$ and
slightly easier parameter combinations in which every algorithm is at best
$2$-competitive. We then design three classes of algorithms and prove they are
$1$, $2$, and $4$-competitive, respectively, for increasingly difficult
parameter combinations. Finally, we present numerical studies that provide
insights into the performance of these algorithms against stochastically
generated intruders.
