### 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 network, assuming an upper bound on the time of any edge traversal by an agent. The minimum number of agents capable to identify a black hole is two. For a given graph and given starting node we are interested in the fastest possible black hole search by two agents, under the general scenario in which some subset of nodes is safe and the black hole can be located in one of the remaining nodes. We show that the problem of finding the fastest possible black hole search scheme by two agents is NP-hard, and we give a 9.3-approximation for it.

Original language | English (US) |
---|---|

Pages (from-to) | 229-242 |

Number of pages | 14 |

Journal | Fundamenta Informaticae |

Volume | 71 |

Issue number | 2-3 |

State | Published - Jun 22 2006 |

Externally published | Yes |

### Fingerprint

### Keywords

- Approximation algorithm
- Black hole
- Graph
- Mobile agent
- NP-hard problem

### ASJC Scopus subject areas

- Theoretical Computer Science
- Algebra and Number Theory
- Information Systems
- Computational Theory and Mathematics

### Cite this

*Fundamenta Informaticae*,

*71*(2-3), 229-242.

**Complexity of searching for a black hole.** / Czyzowicz, Jurek; Kowalski, Dariusz; Markou, Euripides; Pelc, Andrzej.

Research output: Contribution to journal › Article

*Fundamenta Informaticae*, vol. 71, no. 2-3, pp. 229-242.

}

TY - JOUR

T1 - Complexity of searching for a black hole

AU - Czyzowicz, Jurek

AU - Kowalski, Dariusz

AU - Markou, Euripides

AU - Pelc, Andrzej

PY - 2006/6/22

Y1 - 2006/6/22

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 network, assuming an upper bound on the time of any edge traversal by an agent. The minimum number of agents capable to identify a black hole is two. For a given graph and given starting node we are interested in the fastest possible black hole search by two agents, under the general scenario in which some subset of nodes is safe and the black hole can be located in one of the remaining nodes. We show that the problem of finding the fastest possible black hole search scheme by two agents is NP-hard, and we give a 9.3-approximation for it.

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 network, assuming an upper bound on the time of any edge traversal by an agent. The minimum number of agents capable to identify a black hole is two. For a given graph and given starting node we are interested in the fastest possible black hole search by two agents, under the general scenario in which some subset of nodes is safe and the black hole can be located in one of the remaining nodes. We show that the problem of finding the fastest possible black hole search scheme by two agents is NP-hard, and we give a 9.3-approximation for it.

KW - Approximation algorithm

KW - Black hole

KW - Graph

KW - Mobile agent

KW - NP-hard problem

UR - http://www.scopus.com/inward/record.url?scp=33745119003&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745119003&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33745119003

VL - 71

SP - 229

EP - 242

JO - Fundamenta Informaticae

JF - Fundamenta Informaticae

SN - 0169-2968

IS - 2-3

ER -