Time-Optimal Gathering Algorithm of Mobile Robots with Local Weak Multiplicity Detection in Rings

摘要

The gathering problem of anonymous and oblivious mobile robots is one of the fundamental problems in the theoretical mobile robotics. We consider the gathering problem in unoriented and anonymous rings, which requires that all robots eventually keep their positions at a common non-predefined node. Since the gathering problem cannot be solved without any additional capability to robots, all the previous results assume some capability of robots, such as the agreement of local view. In this paper, we focus on the multiplicity detection capability. This paper presents a deterministic gathering algorithm with local-weak multiplicity detection, which provides a robot with information about whether its current node has more than one robot or not. This assumption is strictly weaker than that in previous works. Our algorithm achieves the gathering from an aperiodic and asymmetric configuration with 2<k<n/2 robots, where n is the number of nodes. We also show that our algorithm is asymptotically time-optimal one, i.e., the time complexity of our algorithm is O(n). Interestingly, despite the weaker assumption, it achieves significant improvement compared to the previous algorithm, which takes O(kn) time for k robots.