Hardness and approximation results for Black Hole Search in arbitrary networks

  • Authors:

  • Ralf Klasing;Euripides Markou;Tomasz Radzik;Fabiano Sarracco

  • Affiliations:

  • LaBRI - Université Bordeaux 1 - CNRS, 351 cours de la Libération, 33405 Talence Cedex, France;School of Computational Engineering & Science, McMaster University, 1280 Main St. West, Hamilton, Ontario L8S 4K1, Canada;Department of Computer Science, Kings College London, London, WC2R 2LS, UK;DIS - Dipartimento di Informatica e Sistemistica, CTL - Centro di ricerca per il Trasporto e la Logistica, Sapienza - Università di Roma, Italy

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2007

Quantified Score

Hi-index 5.23

Visualization

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 by exploring it with mobile agents. We consider the problem of designing the fastest Black Hole Search, given the map of the network and the starting node. 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 NP-hard in arbitrary graphs (even in planar graphs), solving an open problem stated in [J. Czyzowicz, D. Kowalski, E. Markou, A. Pelc, Searching for a black hole in tree networks, in: Proc. 8th Int. Conf. on Principles of Distributed Systems, OPODIS 2004, 2004, pp. 34-35. Also: Springer LNCS, vol. 3544, pp. 67-80]. We also give a -approximation algorithm, showing the first non-trivial approximation ratio upper bound for this problem. Our algorithm follows a natural approach of exploring networks via spanning trees. We prove that this approach cannot lead to an approximation ratio bound better than 3/2.