Approximation Bounds for Black Hole Search Problems

  • Ralf Klasing
  • Euripides Markou
  • Tomasz Radzik
  • Fabiano Sarracco
Conference paper

DOI: 10.1007/11795490_21

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3974)
Cite this paper as:
Klasing R., Markou E., Radzik T., Sarracco F. (2006) Approximation Bounds for Black Hole Search Problems. In: Anderson J.H., Prencipe G., Wattenhofer R. (eds) Principles of Distributed Systems. OPODIS 2005. Lecture Notes in Computer Science, vol 3974. Springer, Berlin, Heidelberg

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 

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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

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