### Abstract

A set of k mobile agents with distinct identifiers and located in nodes of an unknown anonymous connected network, have to meet at some node. We show that this gathering problem is no harder than its special case for k = 2, called the rendezvous problem, and design deterministic protocols solving the rendezvous problem with arbitrary startups in rings and in general networks. The measure of performance is the number of steps since the startup of the last agent until the rendezvous is achieved. For rings we design an oblivious protocol with cost O(nlogℓ), where n is the size of the network and ℓ is the minimum label of participating agents. This result is asymptotically optimal due to the lower bound showed in [18]. For general networks we show a protocol with cost polynomial in n and logℓ, independent of the maximum difference τ of startup times, which answers in affirmative the open question from [22].

Original language | English (US) |
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Title of host publication | Structural Information and Communication Complexity - 13th International Colloquium, SIROCCO 2006, Proceedings |

Publisher | Springer Verlag |

Pages | 44-58 |

Number of pages | 15 |

ISBN (Print) | 3540354743, 9783540354741 |

State | Published - Jan 1 2006 |

Externally published | Yes |

Event | 13th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2006 - Chester, United Kingdom Duration: Jul 2 2006 → Jul 5 2006 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4056 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 13th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2006 |
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Country | United Kingdom |

City | Chester |

Period | 7/2/06 → 7/5/06 |

### Fingerprint

### Keywords

- Anonymous networks
- Distributed algorithms
- Gathering
- Mobile agents
- Rendezvous

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Structural Information and Communication Complexity - 13th International Colloquium, SIROCCO 2006, Proceedings*(pp. 44-58). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4056 LNCS). Springer Verlag.

**How to meet in anonymous network.** / Kowalski, Dariusz R.; Malinowski, Adam.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Structural Information and Communication Complexity - 13th International Colloquium, SIROCCO 2006, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4056 LNCS, Springer Verlag, pp. 44-58, 13th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2006, Chester, United Kingdom, 7/2/06.

}

TY - GEN

T1 - How to meet in anonymous network

AU - Kowalski, Dariusz R.

AU - Malinowski, Adam

PY - 2006/1/1

Y1 - 2006/1/1

N2 - A set of k mobile agents with distinct identifiers and located in nodes of an unknown anonymous connected network, have to meet at some node. We show that this gathering problem is no harder than its special case for k = 2, called the rendezvous problem, and design deterministic protocols solving the rendezvous problem with arbitrary startups in rings and in general networks. The measure of performance is the number of steps since the startup of the last agent until the rendezvous is achieved. For rings we design an oblivious protocol with cost O(nlogℓ), where n is the size of the network and ℓ is the minimum label of participating agents. This result is asymptotically optimal due to the lower bound showed in [18]. For general networks we show a protocol with cost polynomial in n and logℓ, independent of the maximum difference τ of startup times, which answers in affirmative the open question from [22].

AB - A set of k mobile agents with distinct identifiers and located in nodes of an unknown anonymous connected network, have to meet at some node. We show that this gathering problem is no harder than its special case for k = 2, called the rendezvous problem, and design deterministic protocols solving the rendezvous problem with arbitrary startups in rings and in general networks. The measure of performance is the number of steps since the startup of the last agent until the rendezvous is achieved. For rings we design an oblivious protocol with cost O(nlogℓ), where n is the size of the network and ℓ is the minimum label of participating agents. This result is asymptotically optimal due to the lower bound showed in [18]. For general networks we show a protocol with cost polynomial in n and logℓ, independent of the maximum difference τ of startup times, which answers in affirmative the open question from [22].

KW - Anonymous networks

KW - Distributed algorithms

KW - Gathering

KW - Mobile agents

KW - Rendezvous

UR - http://www.scopus.com/inward/record.url?scp=33746382915&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746382915&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33746382915

SN - 3540354743

SN - 9783540354741

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 44

EP - 58

BT - Structural Information and Communication Complexity - 13th International Colloquium, SIROCCO 2006, Proceedings

PB - Springer Verlag

ER -