Searching for a Black Hole in Synchronous Tree Networks¶

  • Authors:

  • Jurek Czyzowicz;Dariusz Kowalski;Euripides Markou;Andrzej Pelc

  • Affiliations:

  • Déepartement d'Informatique, Université du Quéebec en Outaouais, Gatineau, Québec J8X 3X7, Canada (e-mail: jurek@uqo.ca, pelc@uqo.ca);Department of Computer Science, The University of Liverpool, Chadwick Building, Peach Street, Liverpool L69 7ZF, UK (e-mail: D.R.Kowalski@csc.liv.ac.uk);Department of Informatics and Telecommunications, National Kapodistrian University of Athens, Panepistimiopolis 15784, Athens, Greece (e-mail: emarkou@di.uoa.gr);Déepartement d'Informatique, Université du Quéebec en Outaouais, Gatineau, Québec J8X 3X7, Canada (e-mail: jurek@uqo.ca, pelc@uqo.ca)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2007

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Abstract

A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node, without leaving any trace. We consider the task of locating a black hole in a (partially) synchronous tree network, assuming an upper bound on the time of any edge traversal by an agent. The minimum number of agents capable of identifying a black hole is two. For a given tree and given starting node we are interested in the fastest-possible black hole search by two agents. For arbitrary trees we give a 5/3-approximation algorithm for this problem. We give optimal black hole search algorithms for two ‘extreme’ classes of trees: the class of lines and the class of trees in which any internal node (including the root which is the starting node) has at least two children.