  The cops-and-robber (CR) game has been used in mobile robotics as a
discretized model (played on a graph G) of pursuit/evasion problems. The
"classic" CR version is a perfect information game: the cops' (pursuer's)
location is always known to the robber (evader) and vice versa. Many variants
of the classic game can be defined: the robber can be invisible and also the
robber can be either adversarial (tries to avoid capture) or drunk (performs a
random walk). Furthermore, the cops and robber can reside in either nodes or
edges of G. Several of these variants are relevant as models or robotic pursuit
/ evasion. In this paper, we first define carefully several of the variants
mentioned above and related quantities such as the cop number and the capture
time. Then we introduce and study the cost of visibility (COV), a quantitative
measure of the increase in difficulty (from the cops' point of view) when the
robber is invisible. In addition to our theoretical results, we present
algorithms which can be used to compute capture times and COV of graphs which
are analytically intractable. Finally, we present the results of applying these
algorithms to the numerical computation of COV.
