### 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) |
---|---|

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 |

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### ASJC Scopus subject areas

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

### Cite this

*Combinatorics Probability and Computing*,

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

**Searching for a black hole in synchronous tree networks.** / Czyzowicz, Jurek; Kowalski, Dariusz; Markou, Euripides; Pelc, Andrzej.

Research output: Contribution to journal › Article

*Combinatorics Probability and Computing*, vol. 16, no. 4, pp. 595-619. https://doi.org/10.1017/S0963548306008133

}

TY - JOUR

T1 - Searching for a black hole in synchronous tree networks

AU - Czyzowicz, Jurek

AU - Kowalski, Dariusz

AU - Markou, Euripides

AU - Pelc, Andrzej

PY - 2007/7/1

Y1 - 2007/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34249980141&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249980141&partnerID=8YFLogxK

U2 - 10.1017/S0963548306008133

DO - 10.1017/S0963548306008133

M3 - Article

AN - SCOPUS:34249980141

VL - 16

SP - 595

EP - 619

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

SN - 0963-5483

IS - 4

ER -