3,102 research outputs found
Visibility Graphs, Dismantlability, and the Cops and Robbers Game
We study versions of cop and robber pursuit-evasion games on the visibility
graphs of polygons, and inside polygons with straight and curved sides. Each
player has full information about the other player's location, players take
turns, and the robber is captured when the cop arrives at the same point as the
robber. In visibility graphs we show the cop can always win because visibility
graphs are dismantlable, which is interesting as one of the few results
relating visibility graphs to other known graph classes. We extend this to show
that the cop wins games in which players move along straight line segments
inside any polygon and, more generally, inside any simply connected planar
region with a reasonable boundary. Essentially, our problem is a type of
pursuit-evasion using the link metric rather than the Euclidean metric, and our
result provides an interesting class of infinite cop-win graphs.Comment: 23 page
Search and Pursuit-Evasion in Mobile Robotics, A survey
This paper surveys recent results in pursuitevasion
and autonomous search relevant to applications
in mobile robotics. We provide a taxonomy of search
problems that highlights the differences resulting from
varying assumptions on the searchers, targets, and the
environment. We then list a number of fundamental
results in the areas of pursuit-evasion and probabilistic
search, and we discuss field implementations on mobile
robotic systems. In addition, we highlight current open
problems in the area and explore avenues for future
work
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