Gracefully Degrading Gathering in Dynamic Rings

Gracefully degrading algorithms [Biely \etal, TCS 2018] are designed to circumvent impossibility results in dynamic systems by adapting themselves to the dynamics. Indeed, such an algorithm solves a given problem under some dynamics and, moreover, guarantees that a weaker (but related) problem is solved under a higher dynamics under which the original problem is impossible to solve. The underlying intuition is to solve the problem whenever possible but to provide some kind of quality of service if the dynamics become (unpredictably) higher.In this paper, we apply for the first time this approach to robot networks. We focus on the fundamental problem of gathering a squad of autonomous robots on an unknown location of a dynamic ring. In this goal, we introduce a set of weaker variants of this problem. Motivated by a set of impossibility results related to the dynamics of the ring, we propose a gracefully degrading gathering algorithm.