We consider a scenario in which n mobile robots with a limited viewing range are distributed arbitrarily in the plane, such that the visibility graph of the robots is connected. The goal is to gather the robots in one (not predefined) point. Each robot may base its decision where to move only on the current relative positions of the robots which are in its viewing range. That is, besides having a limited viewing range, the robots are oblivious (they do not use information from the past), they do not have IDs, and they do not have a common sense of direction. On the other hand side, we assume that they are points, i.e., have no extent.

The problem of gathering n autonomous robots in the Euclidean plane at one (not predefined) point is well-studied under various restrictions on the capabilities of the robots and in several time models. However, only very few runtime bounds are known. We consider the scenario of local algorithms in which the robots can only observe their environment within a fixed viewing range and have to base their decision where to move in the next step solely on the relative positions of the robots within their viewing range. Such local algorithms have to guarantee that the (initially connected) unit disk graph defined by the viewing range of the robots stays connected at all times. In this paper, we focus on the synchronous setting in which all robots are activated concurrently. Ando et al.

We present a distributed, local solution to the dynamic facility location problem in general metrics, where each node is able to act as a facility or a client. To decide which r ole it should take, each node keeps up a simple invariant in its local neighborhood. This guarantees a global constant factor approximation when the invariant is satisfied at all nodes. Due to the changing distances between nodes, invariants can be violated. We show that restoring the invariants is bounded to a constant neighborhood, takes logarithmic (in the number of nodes) asynchronous rounds and affects each node at most twice per violation.

The gathering problem, where n autonomous robots with restricted capabilities are required to meet in a single point of the plane, is widely studied. We consider the case that robots are limited to see only robots within a bounded vicinity and present an algorithm achieving gathering in O(n2) rounds in expectation. A round consists of a movement of all robots, in random order. All previous algorithms with a proven time bound assume global view on the configuration of all robots.