### Abstract

We study three communication primitives in wireless radio networks: Connectivity, One-Receiver, and Gossiping. Radio networks are modeled by undirected graphs of general topology. We consider centralized solutions to the abovementioned problems. In Connectivity and One-Receiver problems, we study the impact of multi-channel assignment to the hardness and approximation of computing of assignments with the minimum number of channels. More precisely, we show that both Connectivity and One-Reciver are Ω(logn)-inapproximable, unless NP ⊂ DTIME(n^{log log n}). We also give polynomial time algorithms computing multi-channel assignments using at most 3(Δ + ln ^{2} n) channels for connectivity and at most Δ channels for one-receiver problem, where n is the number of nodes and Δ is the maximum node degree in the graph. Finally, in case of the classical gossiping problem, related to the connectivity problem, we show that it is NP-complete.

Original language | English (US) |
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Title of host publication | Theory and Practice of Algorithms in (Computer) Systems - First International ICST Conference, TAPAS 2011, Proceedings |

Pages | 181-192 |

Number of pages | 12 |

DOIs | |

State | Published - Apr 14 2011 |

Externally published | Yes |

Event | 1st International ICST Conference on Theory and Practice of Algorithms in (Computer) Systems, TAPAS 2011 - Rome, Italy Duration: Apr 18 2011 → Apr 20 2011 |

### 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 | 6595 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 1st International ICST Conference on Theory and Practice of Algorithms in (Computer) Systems, TAPAS 2011 |
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Country | Italy |

City | Rome |

Period | 4/18/11 → 4/20/11 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theory and Practice of Algorithms in (Computer) Systems - First International ICST Conference, TAPAS 2011, Proceedings*(pp. 181-192). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6595 LNCS). https://doi.org/10.1007/978-3-642-19754-3_19

**Multi-channel assignment for communication in radio networks.** / Kowalski, Dariusz R.; Rokicki, Mariusz A.

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

*Theory and Practice of Algorithms in (Computer) Systems - First International ICST Conference, TAPAS 2011, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6595 LNCS, pp. 181-192, 1st International ICST Conference on Theory and Practice of Algorithms in (Computer) Systems, TAPAS 2011, Rome, Italy, 4/18/11. https://doi.org/10.1007/978-3-642-19754-3_19

}

TY - GEN

T1 - Multi-channel assignment for communication in radio networks

AU - Kowalski, Dariusz R.

AU - Rokicki, Mariusz A.

PY - 2011/4/14

Y1 - 2011/4/14

N2 - We study three communication primitives in wireless radio networks: Connectivity, One-Receiver, and Gossiping. Radio networks are modeled by undirected graphs of general topology. We consider centralized solutions to the abovementioned problems. In Connectivity and One-Receiver problems, we study the impact of multi-channel assignment to the hardness and approximation of computing of assignments with the minimum number of channels. More precisely, we show that both Connectivity and One-Reciver are Ω(logn)-inapproximable, unless NP ⊂ DTIME(nlog log n). We also give polynomial time algorithms computing multi-channel assignments using at most 3(Δ + ln 2 n) channels for connectivity and at most Δ channels for one-receiver problem, where n is the number of nodes and Δ is the maximum node degree in the graph. Finally, in case of the classical gossiping problem, related to the connectivity problem, we show that it is NP-complete.

AB - We study three communication primitives in wireless radio networks: Connectivity, One-Receiver, and Gossiping. Radio networks are modeled by undirected graphs of general topology. We consider centralized solutions to the abovementioned problems. In Connectivity and One-Receiver problems, we study the impact of multi-channel assignment to the hardness and approximation of computing of assignments with the minimum number of channels. More precisely, we show that both Connectivity and One-Reciver are Ω(logn)-inapproximable, unless NP ⊂ DTIME(nlog log n). We also give polynomial time algorithms computing multi-channel assignments using at most 3(Δ + ln 2 n) channels for connectivity and at most Δ channels for one-receiver problem, where n is the number of nodes and Δ is the maximum node degree in the graph. Finally, in case of the classical gossiping problem, related to the connectivity problem, we show that it is NP-complete.

UR - http://www.scopus.com/inward/record.url?scp=79953825777&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79953825777&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-19754-3_19

DO - 10.1007/978-3-642-19754-3_19

M3 - Conference contribution

AN - SCOPUS:79953825777

SN - 9783642197536

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

SP - 181

EP - 192

BT - Theory and Practice of Algorithms in (Computer) Systems - First International ICST Conference, TAPAS 2011, Proceedings

ER -