Forming a connected network in a grid by asynchronous and oblivious robots

Consider an orthogonal grid of streets and avenues in a Manhattan-like city populated by stationary sensor modules at some crossings and mobile robots that can serve as relays of information that the modules exchange. Both module-module and module-robot communication is limited to a straight line of sight along a row or a column of the grid. We present a number of distributed algorithms for the robots to establish a connected network of a given set S of modules by moving to suitable locations in the grid and serving as relays. It is shown that the number of robots required to connect the modules depends not only on the number c of connected components in the visibility graph of S, but also on the degree of symmetry in S. In most cases, our algorithms use the worst case optimal number of robots for a given c.