Almost uniform deployment of mobile agents in dynamic rings

Abstract

In this paper, we consider the almost uniform deployment problem of mobile agents in dynamic rings, which requires all agents other than one agent to spread uniformly in the ring. In this paper, we consider this problem in 1-interval connected rings, that is, one of the links may be missing at each time step. Focusing on global knowledge given to agents, we clarify the problem solvability and the algorithm performance. First, we consider agents with knowledge of the number n of nodes. Then, we show that the problem can be solved with O(klog⁡n) memory space per agent, O(nlog⁡k) rounds, and a total number of O(kn) moves, where k is the number of agents. Next, we consider agents with knowledge of k. Then, we show that the problem can be solved with O(klog⁡n) memory space per agent, O(n2) rounds, and a total number of O(n2) moves.