Black Hole Search with Finite Automata Scattered in a Synchronous Torus

  • Jérémie Chalopin
  • Shantanu Das
  • Arnaud Labourel
  • Euripides Markou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6950)

Abstract

We consider the problem of locating a black hole in synchronous anonymous networks using finite state agents. A black hole is a harmful node in the network that destroys any agent visiting that node without leaving any trace. The objective is to locate the black hole without destroying too many agents. This is difficult to achieve when the agents are initially scattered in the network and are unaware of the location of each other. In contrast to previous results, we solve the problem using a small team of finite-state agents each carrying a constant number of identical tokens that could be placed on the nodes of the network. Thus, all resources used in our algorithms are independent of the network size.

We restrict our attention to oriented torus networks and first show that no finite team of finite state agents can solve the problem in such networks, when the tokens are not movable, i.e., they cannot be moved by the agents once they have been released on a node. In case the agents are equipped with movable tokens, we determine lower bounds on the number of agents and tokens required for solving the problem in torus networks of arbitrary size. Further, we present a deterministic solution to the black hole search problem for oriented torus networks, using the minimum number of agents and tokens, thus providing matching upper bounds for the problem.

Keywords

Black Hole Mobile Agent Token Model Torus Network Empty Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jérémie Chalopin
    • 1
  • Shantanu Das
    • 1
  • Arnaud Labourel
    • 1
  • Euripides Markou
    • 2
  1. 1.LIF, Aix-Marseille UniversityMarseilleFrance
  2. 2.Department of Computer Science and Biomedical InformaticsUniversity of Central GreeceLamiaGreece

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