Hostname: page-component-77c78cf97d-lmk9j Total loading time: 0 Render date: 2026-04-27T01:16:32.828Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access Rights & Permissions [Opens in a new window]

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.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1]Dobrev, S., Flocchini, P., Kralovic, R., Prencipe, G.Ruzicka, P. and Santoro, N. (2002) Black hole search by mobile agents in hypercubes and related networks. In Proc. 6th Int. Conference on Principles of Distributed Systems (OPODIS 2002), pp. 171–182.Google Scholar
[2]Dobrev, S., Flocchini, P., Prencipe, G. and Santoro, N. (2001) Mobile agents searching for a black hole in an anonymous ring. In Proc. 15th International Symposium on Distributed Computing (DISC 2001), Vol. 2180 of Lecture Notes in Computer Science, Springer, pp. 166–179.Google Scholar
[3]Dobrev, S., Flocchini, P., Prencipe, G. and Santoro, N. (2002) Searching for a black hole in arbitrary networks: Optimal Mobile Agents Protocols. In Proc. 21st ACM Symposium on Principles of Distributed Computing (PODC 2002), pp. 153–161.CrossRefGoogle Scholar
[4]Dobrev, S., Flocchini, P., Prencipe, G. and Santoro, N. (2003) Multiple agents rendezvous on a ring in spite of a black hole. In Proc. 7th Int. Conference on Principles of Distributed Systems (OPODIS 2003), Vol. 3144 of Lecture Notes in Computer Science, Springer, pp. 34–46.Google Scholar
[5]Hohl, F. (1998) Time limited black box security: Protecting mobile agents from malicious hosts. In Proc. Conf. on Mobile Agent Security (1998), Vol. 1419 of Lecture Notes in Computer Science, Springer, pp. 92–113.CrossRefGoogle Scholar
[6]Hohl, F. (2000) A framework to protect mobile agents by using reference states. In Proc. 20th Int. Conf. on Distributed Computing Systems (ICDCS 2000), pp. 410–417.CrossRefGoogle Scholar
[7]Klasing, R., Markou, E., Radzik, T. and Sarracco, F. Hardness and approximation results for black hole search in arbitrary networks. Theoret. Comput. Sci., to appear.Google Scholar
[8]Ng, S. and Cheung, K. (1999) Protecting mobile agents against malicious hosts by intention of spreading. In Proc. Int. Conf. on Parallel and Distributed Processing and Applications (PDPTA'99), Vol. II (Arabnia, H., ed.), pp. 725–729.Google Scholar
[9]Sander, T. and Tschudin, C. F. (1998) Protecting mobile agents against malicious hosts. In Proc. Conf. on Mobile Agent Security (Vigna, G., ed.), Vol. 1419 of Lecture Notes in Computer Science, Springer, pp. 44–60.CrossRefGoogle Scholar
[10]Schelderup, K. and Ines, J. (1999) Mobile agent security: Issues and directions. In Proc. 6th Int. Conf. on Intelligence and Services in Networks, Vol. 1597 of Lecture Notes in Computer Science, Springer, pp. 155–167.Google Scholar
[11]Vitek, J. and Castagna, G. (1999) Mobile computations and hostile hosts. In Proc. Journées Francophones des Langages Applicatifs (JFLA 1999).Google Scholar