Fault-tolerant mutual visibility without any axis agreement in presence of mobility failure

Abstract

We aim to solve the mutual visibility problem using N autonomous, indistinguishable, homogeneous, oblivious and opaque point robots in the presence of mobility failure. The faulty robot cannot move when it becomes faulty, but the light remains working. Initially, from any arbitrary configuration, the problem of mutual visibility using robots aims to reach a configuration where any two robots can see each other. The challenge is to reach to such a configuration in the presence of faulty robots along with obstructed visibility under which two robots see each other only if the line segment joining them does not have any robots. Every robot operates in the conventional Look-Compute-Move cycles. Robots neither have any agreement in their coordinate system nor have the knowledge of N. The problem is not solvable for a specific symmetric initial configuration of the robots. We propose an algorithm that tolerates $f(\le N)$ number of faulty robots and uses a constant number of colors in the FSYNC setting. To be specific, the algorithm requires 21 colors and runs in $O\left(N^2\right)$ synchronous rounds. We present another algorithm much simpler than the prior one but can tolerate a single faulty robot. This algorithm needs only 2 colors in the SSYNC and 5 colors in the ASYNC setting.