### 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.

Original language | English (US) |
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Pages (from-to) | 595-619 |

Number of pages | 25 |

Journal | Combinatorics Probability and Computing |

Volume | 16 |

Issue number | 4 |

DOIs | |

State | Published - Jul 1 2007 |

Externally published | Yes |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

*Combinatorics Probability and Computing*,

*16*(4), 595-619. https://doi.org/10.1017/S0963548306008133