We consider the distributed setting of
N autonomous mobile robots that operate in
Look-Compute-Move (LCM) cycles following the well-celebrated classic oblivious robots model. We study the fundamental problem of gathering
N autonomous robots on a plane, which requires all robots to meet at
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We consider the distributed setting of
N autonomous mobile robots that operate in
Look-Compute-Move (LCM) cycles following the well-celebrated classic oblivious robots model. We study the fundamental problem of gathering
N autonomous robots on a plane, which requires all robots to meet at a single point (or to position within a small area) that is not known beforehand. We consider limited visibility under which robots are only able to see other robots up to a constant Euclidean distance and focus on the time complexity of gathering by robots under limited visibility. There exists an
time algorithm for this problem in the fully synchronous setting, assuming that the robots agree on one coordinate axis (say north), where
is the diameter of the visibility graph of the initial configuration. In this article, we provide the first
time algorithm for this problem in the asynchronous setting under the same assumption of robots’ agreement with one coordinate axis, where
is the Euclidean distance between farthest-pair of robots in the initial configuration. The runtime of our algorithm is a significant improvement since for any initial configuration of
robots,
, and there exist initial configurations for which
can be quadratic on
, i.e.,
. Moreover, our algorithm is asymptotically time-optimal since the trivial time lower bound for this problem is
.
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