Approximation Bounds for Black Hole Search Problems

  • Ralf Klasing
  • Euripides Markou
  • Tomasz Radzik
  • Fabiano Sarracco
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3974)

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. The Black Hole Search is the task of locating all black holes in a network, through the exploration of its nodes by a set of mobile agents. In this paper we consider the problem of designing the fastest Black Hole Search, given the map of the network, the starting node and, possibly, a subset of nodes of the network initially known to be safe. We study the version of this problem that assumes that there is at most one black hole in the network and there are two agents, which move in synchronized steps. We prove that this problem is not polynomial-time approximable within \(\frac{389}{388}\) (unless P=NP). We give a 6-approximation algorithm, thus improving on the 9.3-approximation algorithm from [3]. We also prove APX-hardness for a restricted version of the problem, in which only the starting node is initially known to be safe.

Keywords

approximation algorithm black hole search graph exploration mobile agent inapproximability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Csaba, B., Karpinski, M., Krysta, P.: Approximability of dense and sparse instances of minimum 2-connectivity, TSP and path problems. In: SODA 2002: Proceedings of the thirteenth annual ACM-SIAM Symposium on Discrete algorithms, Philadelphia, PA, USA, pp. 74–83 (2002)Google Scholar
  2. 2.
    Czyzowicz, J., Kowalski, D., Markou, E., Pelc, A.: Searching for a black hole in tree networks. In: Higashino, T. (ed.) OPODIS 2004. LNCS, vol. 3544, pp. 67–80. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Czyzowicz, J., Kowalski, D., Markou, E., Pelc, A.: Complexity of searching for a black hole. Fundamenta Informaticae (to appear, 2006)Google Scholar
  4. 4.
    Dobrev, S., Flocchini, P., Kralovic, R., Prencipe, G., Ruzicka, P., Santoro, N.: Black hole search by mobile agents in hypercubes and related networks. In: Proc. 6th Int. Conf. on Principles of Distributed Systems (OPODIS 2002), pp. 169–180 (2002)Google Scholar
  5. 5.
    Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Mobile agents searching for a black hole in an anonymous ring. In: Welch, J.L. (ed.) DISC 2001. LNCS, vol. 2180, pp. 166–179. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: 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 (2002)Google Scholar
  7. 7.
    Engebretsen, L., Karpinski, M.: TSP with bounded metrics: stronger approximation hardness. Technical Report 85264, University of Bonn (February 2005)Google Scholar
  8. 8.
    Hohl, F.: Time limited black box security: Protecting mobile agents from malicious hosts. In: Vigna, G. (ed.) Mobile Agents and Security. LNCS, vol. 1419, pp. 92–113. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  9. 9.
    Hohl, F.: A framework to protect mobile agents by using reference states. In: Proc. 20th Int. Conf. on Distributed Computing Systems (ICDCS 2000), pp. 410–417 (2000)Google Scholar
  10. 10.
    Klasing, R., Markou, E., Radzik, T., Sarracco, F.: Hardness and approximation results for black hole search in arbitrary graphs. In: Pelc, A., Raynal, M. (eds.) SIROCCO 2005. LNCS, vol. 3499, pp. 200–215. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Ng, S., Cheung, K.: Protecting mobile agents against malicious hosts by intention of spreading. In: Arabnia, H. (ed.) Proc. Int. Conf. on Parallel and Distributed Processing and Applications (PDPTA 1999), vol. II, pp. 725–729 (1999)Google Scholar
  12. 12.
    Sander, T., Tschudin, C.F.: Protecting mobile agents against malicious hosts. In: Vigna, G. (ed.) Mobile Agents and Security. LNCS, vol. 1419, pp. 44–60. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  13. 13.
    Schelderup, K., Olnes, J.: Mobile agent security – issues and directions. In: Zuidweg, H., Campolargo, M., Delgado, J., Mullery, A. (eds.) IS&N 1999. LNCS, vol. 1597, pp. 155–167. Springer, Heidelberg (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ralf Klasing
    • 1
  • Euripides Markou
    • 2
  • Tomasz Radzik
    • 3
  • Fabiano Sarracco
    • 4
  1. 1.LaBRI – Université Bordeaux 1TalenceFrance
  2. 2.Department of Informatics and TelecommunicationsNational and Kapodistrian University of AthensGreece
  3. 3.Department of Computer ScienceKing’s College LondonLondonUK
  4. 4.Dipartimento di Informatica e SistemisticaUniversità di Roma “La Sapienza”Italy

Personalised recommendations