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 can be thought of as a mobile fault in the network. 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).
S. Das—This work has been partially supported by the ANR - MACARON project (anr-13-js02-0002).
F.L. Luccio—This work has been partially supported by the PRIN 2010 Project Security Horizons.
E. Markou—Part of this work has been done while this author was visiting Università Ca’ Foscari Venezia. This research has been co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) — Research Funding Program: THALIS-NTUA (MIS 379414).
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Notes
- 1.
We select as searcher the second agent that arrives at node v.
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Das, S., Luccio, F.L., Markou, E. (2015). Mobile Agents Rendezvous in Spite of a Malicious Agent. In: Bose, P., Gąsieniec, L., Römer, K., Wattenhofer, R. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2015. Lecture Notes in Computer Science(), vol 9536. Springer, Cham. https://doi.org/10.1007/978-3-319-28472-9_16
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