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Hardness and Approximation Results for Black Hole Search in Arbitrary Graphs

  • Ralf Klasing
  • Euripides Markou
  • Tomasz Radzik
  • Fabiano Sarracco
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3499)

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 arbitrary network, assuming an upper bound on the time of any edge traversal by an agent. For a given graph and a given starting node we are interested in finding the fastest possible Black Hole Search by two agents (the minimum number of agents capable to identify a black hole). We prove that this problem is NP-hard in arbitrary graphs, thus solving an open problem stated in [2]. We also give a 7/2-approximation algorithm, thus improving on the 4-approximation scheme observed in [2]. Our approach is to explore the given input graph via some spanning tree. Even if it represents a very natural technique, we prove that this approach cannot achieve an approximation ratio better than 3/2.

Keywords

approximation algorithm black hole search graph exploration mobile agent NP-hardness 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ralf Klasing
    • 1
  • Euripides Markou
    • 2
  • Tomasz Radzik
    • 3
  • Fabiano Sarracco
    • 4
  1. 1.MASCOTTE projectI3S-CNRS/INRIA/Université de Nice-Sophia AntipolisSophia Antipolis CedexFrance
  2. 2.Department of Informatics and TelecommunicationsNational and Kapodistrian University of Athens 
  3. 3.Department of Computer ScienceKing’s College LondonLondonUK
  4. 4.Dipartimento di Informatica e SistemisticaUniversità di Roma “La Sapienza” 

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