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Searching for a Black Hole in Synchronous Tree Networks

Published online by Cambridge University Press:  01 July 2007

JUREK CZYZOWICZ ,
DARIUSZ KOWALSKI ,
EURIPIDES MARKOU  and
ANDRZEJ PELC
JUREK CZYZOWICZ
Affiliation:
Déepartement d'Informatique, Université du Quéebec en Outaouais, Gatineau, Québec J8X 3X7, Canada (e-mail: jurek@uqo.ca, pelc@uqo.ca)
DARIUSZ KOWALSKI
Affiliation:
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)
EURIPIDES MARKOU
Affiliation:
Department of Informatics and Telecommunications, National Kapodistrian University of Athens, Panepistimiopolis 15784, Athens, Greece (e-mail: emarkou@di.uoa.gr)
ANDRZEJ PELC
Affiliation:
Déepartement d'Informatique, Université du Quéebec en Outaouais, Gatineau, Québec J8X 3X7, Canada (e-mail: jurek@uqo.ca, pelc@uqo.ca)
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Abstract

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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.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 16 , Issue 4 , July 2007 , pp. 595 - 619
Copyright
Copyright © Cambridge University Press 2006

References

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