Uniform Deployment of Mobile Agents in Dynamic Rings

Abstract

In this paper, we consider the uniform deployment problem of mobile agents in synchronous dynamic bidirectional rings, which requires agents to spread uniformly in the ring. So far, uniform deployment has been considered in static graphs. 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. In such networks, we aim to clarify the solvability of the uniform deployment problem, focusing on global knowledge given to the agents. To the best of our knowledge, this is the first research considering uniform deployment in dynamic networks. First, we consider agents with knowledge of the number n of nodes. In this case, we show that our algorithm can solve the problem with $O(k\log n)$ memory space per agent, $O(n\log k)$ rounds, and a total number of O(kn) moves, where k is the number of agents. Next, we consider agents without knowledge of n but with knowledge of k. In this case, when $k\ge 4$, we show that our algorithm can also solve the problem but requires $O(k\log n)$ memory space per agent, $O(n^2)$ rounds, and a total number of $O(n^2)$ moves. These results mean that the uniform deployment problem can be solved also in dynamic rings.