1 research outputs found
Guarding a Polygon Without Losing Touch
We study the classical Art Gallery Problem first proposed by Klee in 1973
from a mobile multi-agents perspective. Specifically, we require an optimally
small number of agents (also called guards) to navigate and position themselves
in the interior of an unknown simple polygon with vertices such that the
collective view of all the agents covers the polygon.
We consider the visibly connected setting wherein agents must remain
connected through line of sight links -- a requirement particularly relevant to
multi-agent systems. We first provide a centralized algorithm for the visibly
connected setting that runs in time , which is of course optimal. We then
provide algorithms for two different distributed settings. In the first
setting, agents can only perceive relative proximity (i.e., can tell which of a
pair of objects is closer) whereas they can perceive exact distances in the
second setting. Our distributed algorithms work despite agents having no prior
knowledge of the polygon. Furthermore, we provide lower bounds to show that our
distributed algorithms are near-optimal.
Our visibly connected guarding ensures that (i) the guards form a connected
network and (ii) the polygon is fully guarded. Consequently, this guarding
provides the distributed infrastructure to execute any geometric algorithm for
this polygon