### 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 (n log ℓ), 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 by [A. Dessmark, P. Fraigniaud, D. Kowalski, A. Pelc, Deterministic rendezvous in graphs, Algorithmica 46 (2006) 69-96]. For general networks we show a protocol with cost polynomial in n and log ℓ, independent of the maximum difference τ of startup times, which answers in the affirmative the open question by [A. Dessmark, P. Fraigniaud, D. Kowalski, A. Pelc, Deterministic rendezvous in graphs, Algorithmica 46 (2006) 69-96].

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

Pages (from-to) | 141-156 |

Number of pages | 16 |

Journal | Theoretical Computer Science |

Volume | 399 |

Issue number | 1-2 |

DOIs | |

State | Published - Jun 3 2008 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

*399*(1-2), 141-156. https://doi.org/10.1016/j.tcs.2008.02.010

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

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 399, no. 1-2, pp. 141-156. https://doi.org/10.1016/j.tcs.2008.02.010

}

TY - JOUR

T1 - How to meet in anonymous network

AU - Kowalski, Dariusz R.

AU - Malinowski, Adam

PY - 2008/6/3

Y1 - 2008/6/3

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 (n log ℓ), 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 by [A. Dessmark, P. Fraigniaud, D. Kowalski, A. Pelc, Deterministic rendezvous in graphs, Algorithmica 46 (2006) 69-96]. For general networks we show a protocol with cost polynomial in n and log ℓ, independent of the maximum difference τ of startup times, which answers in the affirmative the open question by [A. Dessmark, P. Fraigniaud, D. Kowalski, A. Pelc, Deterministic rendezvous in graphs, Algorithmica 46 (2006) 69-96].

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 (n log ℓ), 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 by [A. Dessmark, P. Fraigniaud, D. Kowalski, A. Pelc, Deterministic rendezvous in graphs, Algorithmica 46 (2006) 69-96]. For general networks we show a protocol with cost polynomial in n and log ℓ, independent of the maximum difference τ of startup times, which answers in the affirmative the open question by [A. Dessmark, P. Fraigniaud, D. Kowalski, A. Pelc, Deterministic rendezvous in graphs, Algorithmica 46 (2006) 69-96].

KW - Anonymous networks

KW - Distributed algorithms

KW - Gathering

KW - Mobile agents

KW - Rendezvous

UR - http://www.scopus.com/inward/record.url?scp=42749093516&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42749093516&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2008.02.010

DO - 10.1016/j.tcs.2008.02.010

M3 - Article

AN - SCOPUS:42749093516

VL - 399

SP - 141

EP - 156

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 1-2

ER -