Black Hole Search with Finite Automata Scattered in a Synchronous Torus View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2011

AUTHORS

Jérémie Chalopin , Shantanu Das , Arnaud Labourel , Euripides Markou

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. More... »

PAGES

432-446

References to SciGraph publications

  • 2008. Ping Pong in Dangerous Graphs: Optimal Black Hole Search with Pure Tokens in DISTRIBUTED COMPUTING
  • 2010. Periodic Data Retrieval Problem in Rings Containing a Malicious Host in STRUCTURAL INFORMATION AND COMMUNICATION COMPLEXITY
  • 2010. Black Hole Search in Directed Graphs in STRUCTURAL INFORMATION AND COMMUNICATION COMPLEXITY
  • 2006. Black Hole Search in Asynchronous Rings Using Tokens in ALGORITHMS AND COMPLEXITY
  • 2004. Multiple Agents RendezVous in a Ring in Spite of a Black Hole in PRINCIPLES OF DISTRIBUTED SYSTEMS
  • 2007-05. Mobile Search for a Black Hole in an Anonymous Ring in ALGORITHMICA
  • 2006. Searching for Black-Hole Faults in a Network Using Multiple Agents in PRINCIPLES OF DISTRIBUTED SYSTEMS
  • 2009. Black Hole Search with Tokens in Interconnected Networks in STABILIZATION, SAFETY, AND SECURITY OF DISTRIBUTED SYSTEMS
  • 2004. Improved Bounds for Optimal Black Hole Search with a Network Map in STRUCTURAL INFORMATION AND COMMUNICATION COMPLEXITY
  • 2009. Synchronization Helps Robots to Detect Black Holes in Directed Graphs in PRINCIPLES OF DISTRIBUTED SYSTEMS
  • 2011. Tight Bounds for Scattered Black Hole Search in a Ring in STRUCTURAL INFORMATION AND COMMUNICATION COMPLEXITY
  • 2006-09. Searching for a black hole in arbitrary networks: optimal mobile agents protocols in DISTRIBUTED COMPUTING
  • 2007. Rendezvous of Mobile Agents in Unknown Graphs with Faulty Links in DISTRIBUTED COMPUTING
  • 2009. Locating a Black Hole without the Knowledge of Incoming Link in ALGORITHMIC ASPECTS OF WIRELESS SENSOR NETWORKS
  • Book

    TITLE

    Distributed Computing

    ISBN

    978-3-642-24099-7
    978-3-642-24100-0

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-642-24100-0_41

    DOI

    http://dx.doi.org/10.1007/978-3-642-24100-0_41

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1040614882


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    31 schema:description 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.
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