### Abstract

Radio networks model wireless synchronous communication with only one wave frequency used for transmissions. In the problem of many-to-all (M2A) communication, some nodes hold input rumors, and the goal is to have all nodes learn all the rumors. We study the average time complexity of distributed many-to-all communication by deterministic protocols in directed networks under two scenarios: of combined messages, in which all input rumors can be sent in one packet, and of separate messages, in which every rumor requires a separate packet to be transmitted. Let n denote the size of a network and k be the number of nodes activated with rumors; the case when k = n is called gossiping. We give & gossiping protocol for combined messages that works in the average time script O sign(n/log n), which is shown to be optimal. For the general M2A communication problem, we show that it can be performed in the average time script O sign(min{k log(n/k),n/log n}) with combined messages, and that Ω(k/log n + log n) is a lower bound. We give a gossiping protocol for separate messages that works in the average time script O sign(n log n), which is shown to be optimal. For the general M2A communication problem, we develop a protocol for separate messages with the average time script O sign(k log(n/k) log n), and show that Ω(k log n) is a lower bound.

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 | 253-267 |

Number of pages | 15 |

ISBN (Print) | 3540354743, 9783540354741 |

DOIs | |

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

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Structural Information and Communication Complexity - 13th International Colloquium, SIROCCO 2006, Proceedings*(pp. 253-267). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4056 LNCS). Springer Verlag. https://doi.org/10.1007/11780823_20

**Average-time complexity of gossiping in radio networks.** / Chlebus, Bogdan S.; Kowalski, Dariusz R.; Rokicki, Mariusz A.

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. 253-267, 13th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2006, Chester, United Kingdom, 7/2/06. https://doi.org/10.1007/11780823_20

}

TY - GEN

T1 - Average-time complexity of gossiping in radio networks

AU - Chlebus, Bogdan S.

AU - Kowalski, Dariusz R.

AU - Rokicki, Mariusz A.

PY - 2006/1/1

Y1 - 2006/1/1

N2 - Radio networks model wireless synchronous communication with only one wave frequency used for transmissions. In the problem of many-to-all (M2A) communication, some nodes hold input rumors, and the goal is to have all nodes learn all the rumors. We study the average time complexity of distributed many-to-all communication by deterministic protocols in directed networks under two scenarios: of combined messages, in which all input rumors can be sent in one packet, and of separate messages, in which every rumor requires a separate packet to be transmitted. Let n denote the size of a network and k be the number of nodes activated with rumors; the case when k = n is called gossiping. We give & gossiping protocol for combined messages that works in the average time script O sign(n/log n), which is shown to be optimal. For the general M2A communication problem, we show that it can be performed in the average time script O sign(min{k log(n/k),n/log n}) with combined messages, and that Ω(k/log n + log n) is a lower bound. We give a gossiping protocol for separate messages that works in the average time script O sign(n log n), which is shown to be optimal. For the general M2A communication problem, we develop a protocol for separate messages with the average time script O sign(k log(n/k) log n), and show that Ω(k log n) is a lower bound.

AB - Radio networks model wireless synchronous communication with only one wave frequency used for transmissions. In the problem of many-to-all (M2A) communication, some nodes hold input rumors, and the goal is to have all nodes learn all the rumors. We study the average time complexity of distributed many-to-all communication by deterministic protocols in directed networks under two scenarios: of combined messages, in which all input rumors can be sent in one packet, and of separate messages, in which every rumor requires a separate packet to be transmitted. Let n denote the size of a network and k be the number of nodes activated with rumors; the case when k = n is called gossiping. We give & gossiping protocol for combined messages that works in the average time script O sign(n/log n), which is shown to be optimal. For the general M2A communication problem, we show that it can be performed in the average time script O sign(min{k log(n/k),n/log n}) with combined messages, and that Ω(k/log n + log n) is a lower bound. We give a gossiping protocol for separate messages that works in the average time script O sign(n log n), which is shown to be optimal. For the general M2A communication problem, we develop a protocol for separate messages with the average time script O sign(k log(n/k) log n), and show that Ω(k log n) is a lower bound.

UR - http://www.scopus.com/inward/record.url?scp=33746382287&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746382287&partnerID=8YFLogxK

U2 - 10.1007/11780823_20

DO - 10.1007/11780823_20

M3 - Conference contribution

AN - SCOPUS:33746382287

SN - 3540354743

SN - 9783540354741

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

SP - 253

EP - 267

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

PB - Springer Verlag

ER -