(Georgia Institute of Technology, 2001)
Koenig, Sven; Halliburton, William; Tovey, Craig A.
We study a greedy mapping method that always moves the
robot from its current location to the closest location that it has
not visited (or observed) yet, until the terrain is mapped. Although
one does not expect such a simple mapping method to minimize
the travel distance of the robot, we present analytical results that
show (perhaps surprisingly) that the travel distance of the robot is
reasonably small. This is interesting because greedy mapping has
a number of desirable properties. It is simple to implement and integrate
into complete robot architectures. It does not need to have
control of the robot at all times, takes advantage of prior knowledge
about parts of the terrain (if available), and can be used by
several robots cooperatively.
(Georgia Institute of Technology, 1995-09)
Calkin, Neil J.; Erdös, Paul; Tovey, Craig A.
We present new explicit lower bounds for some Ramsey numbers.
All the graphs are cyclic, and are on a prime number of vertices. We give a
partial probabilistic analysis which suggests that the cyclic Ramsey numbers
grow exponentially. We show that the standard expectation arguments are
insu cient to prove such a result. These arguments motivated our searching
for Ramsey graphs of prime order.