Mobile Agents Rendezvous in spite of a Malicious Agent

TL;DR

This paper investigates the challenge of achieving rendezvous among mobile agents in networks despite the presence of a malicious, highly capable adversary that can move freely and block honest agents, introducing new algorithms and impossibility results.

Contribution

It introduces the first study of rendezvous with a powerful mobile malicious agent, providing algorithms for rings and meshes and establishing necessary conditions and impossibility results.

Findings

Rendezvous algorithms succeed in all feasible instances on rings.

Impossible to achieve rendezvous with an even number of agents in unoriented rings.

Rendezvous is possible in oriented meshes if initial configurations are connected without holes.

Abstract

We examine the problem of rendezvous, i.e., having multiple mobile agents gather in a single node of the network. Unlike previous studies, we need to achieve rendezvous in presence of a very powerful adversary, a malicious agent that moves through the network and tries to block the honest agents and prevents them from gathering. The malicious agent is assumed to be arbitrarily fast, has full knowledge of the network and it cannot be exterminated by the honest agents. On the other hand, the honest agents are assumed to be quite weak: They are asynchronous and anonymous, they have only finite memory, they have no prior knowledge of the network and they can communicate with the other agents only when they meet at a node. Can the honest agents achieve rendezvous starting from an arbitrary configuration in spite of the malicious agent? We present some necessary conditions for solving rendezvous in spite of the malicious agent in arbitrary networks. We then focus on the ring and mesh topologies and provide algorithms to solve rendezvous. For ring networks, our algorithms solve rendezvous in all feasible instances of the problem, while we show that rendezvous is impossible for an even number of agents in unoriented rings. For the oriented mesh networks, we prove that the problem can be solved when the honest agents initially form a connected configuration without holes if and only if they can see which are the occupied nodes within a two-hops distance. To the best of our knowledge, this is the first attempt to study such a powerful and mobile fault model, in the context of mobile agents. Our model lies between the more powerful but static fault model of black holes (which can even destroy the agents), and the less powerful but mobile fault model of Byzantine agents (which can only imitate the honest agents but can neither harm nor stop them).