Mobile Agents Rendezvous in spite of a Malicious Agent

We consider a number of `honest' mobile agents which are initially scattered in an asynchronous network. In the network there is also a hostile mobile agent that is able to block the agents' movements. The honest agents need to meet (rendezvous) at a node. We study this problem under a weakest scenario in which the agents do not have any information about the size of the network or their number, they do not have distinct identities, they cannot see or communicate with each-other unless they are at the same node, and they only have constant memory. We give a universal distributed deterministic algorithm that solves the problem for any number of more than two honest agents in oriented rings, and for any odd number of agents in unoriented rings, despite the existence of a malicious agent. We prove that the problem is unsolvable in any other configuration in a ring network. Then, we study the problem in an oriented mesh network and we prove that the problem can be solved if and only if the honest agents initially form a connected configuration without holes and they can see at a distance two. To the best of our knowledge, this is the first attempt to study such a weak setting with a malicious agent in which the aim of the honest agents is to achieve a task in the `trusted' subnetwork, i.e., in the part of the network where the malicious agent has no access.