Asynchronous Line Formation in Presence of Faulty Robots

In this paper, we study the line formation problem using n oblivious point mobile robots located on distinct positions on the Euclidean plane. We assume that the robots agree on one coordinate axis. Robots operate in Look-Compute-Move (LCM) cycles and any two robots can see each other only if there is no robot present on the line segment joining them. Our aim is to solve the line formation problem even if some robots become faulty before achieving the goal. The robots cannot move anymore once they become faulty. We present a fault-tolerant distributed algorithm for line formation under y-axis agreement which runs in O(n) epochs in semi-synchronous setting. The same algorithm runs in D/ymin epochs in asynchronous setting, where D is the vertical distance between the farthest robots along the y-axis and ymin is the minimum non-zero vertical distance traveled by a robot in each LCM cycle.