Space-efficient uniform deployment of mobile agents in asynchronous unidirectional rings

Abstract

In this paper, we consider the uniform deployment problem of mobile agents in asynchronous unidirectional ring networks. This problem requires agents to spread uniformly in the network. In this paper, we focus on the memory space per agent required to solve the problem. We consider two problem settings. The first setting assumes that agents have no multiplicity detection, that is, agents cannot detect whether another agent is staying at the same node or not. In this case, we show that each agent requires Ω(log n) memory space to solve the problem, where n is the number of nodes. In addition, we propose an algorithm to solve the problem with O(k + log n) memory space per agent, where k is the number of agents. The second setting assumes that each agent is equipped with the weak multiplicity detection, that is, agents can detect another agent staying at the same node, but cannot learn the exact number. Then, we show that the memory space per agent can be reduced to O(log k + log log n). To the best of our knowledge, this is the first research considering the effect of the multiplicity detection on memory space required to solve problems.