### Abstract

We study the complexity of the following connectivity problem in wireless networks: for a given placement of n nodes in the plane, the goal is to compute a channel and power assignment that forms strongly connected communication structure spanning all nodes. The complexity measure is the total number of assigned channels, and the goal is to minimize this number. We work with two signal inference models: Geometric Radio Networks (GRN) and Signal to Interference Plus Noise Ratio (SINR). We show a generic polynomial-time transformation from the wide class of separable assignments in GRN to assignments in the SIRN model. This transformation preserves asymptotic complexity, i.e., the number of channels used in the assignments. In this way we show an assignment, constructed in polynomial-time, guarantying connectivity in the SINR model by using only O(log n) channels, which is an improvement over the best previous result O(log^{2} n) presented in [21].

Original language | English (US) |
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Title of host publication | Distributed Computing - 24th International Symposium, DISC 2010, Proceedings |

Pages | 344-358 |

Number of pages | 15 |

DOIs | |

State | Published - Dec 13 2010 |

Externally published | Yes |

Event | 24th International Symposium on Distributed Computing, DISC 2010 - Cambridge, MA, United States Duration: Sep 13 2010 → Sep 15 2010 |

### 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 | 6343 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 24th International Symposium on Distributed Computing, DISC 2010 |
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Country | United States |

City | Cambridge, MA |

Period | 9/13/10 → 9/15/10 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Distributed Computing - 24th International Symposium, DISC 2010, Proceedings*(pp. 344-358). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6343 LNCS). https://doi.org/10.1007/978-3-642-15763-9_32

**Connectivity problem in wireless networks.** / Kowalski, Dariusz R.; Rokicki, Mariusz A.

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

*Distributed Computing - 24th International Symposium, DISC 2010, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6343 LNCS, pp. 344-358, 24th International Symposium on Distributed Computing, DISC 2010, Cambridge, MA, United States, 9/13/10. https://doi.org/10.1007/978-3-642-15763-9_32

}

TY - GEN

T1 - Connectivity problem in wireless networks

AU - Kowalski, Dariusz R.

AU - Rokicki, Mariusz A.

PY - 2010/12/13

Y1 - 2010/12/13

N2 - We study the complexity of the following connectivity problem in wireless networks: for a given placement of n nodes in the plane, the goal is to compute a channel and power assignment that forms strongly connected communication structure spanning all nodes. The complexity measure is the total number of assigned channels, and the goal is to minimize this number. We work with two signal inference models: Geometric Radio Networks (GRN) and Signal to Interference Plus Noise Ratio (SINR). We show a generic polynomial-time transformation from the wide class of separable assignments in GRN to assignments in the SIRN model. This transformation preserves asymptotic complexity, i.e., the number of channels used in the assignments. In this way we show an assignment, constructed in polynomial-time, guarantying connectivity in the SINR model by using only O(log n) channels, which is an improvement over the best previous result O(log2 n) presented in [21].

AB - We study the complexity of the following connectivity problem in wireless networks: for a given placement of n nodes in the plane, the goal is to compute a channel and power assignment that forms strongly connected communication structure spanning all nodes. The complexity measure is the total number of assigned channels, and the goal is to minimize this number. We work with two signal inference models: Geometric Radio Networks (GRN) and Signal to Interference Plus Noise Ratio (SINR). We show a generic polynomial-time transformation from the wide class of separable assignments in GRN to assignments in the SIRN model. This transformation preserves asymptotic complexity, i.e., the number of channels used in the assignments. In this way we show an assignment, constructed in polynomial-time, guarantying connectivity in the SINR model by using only O(log n) channels, which is an improvement over the best previous result O(log2 n) presented in [21].

UR - http://www.scopus.com/inward/record.url?scp=78649863855&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649863855&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-15763-9_32

DO - 10.1007/978-3-642-15763-9_32

M3 - Conference contribution

AN - SCOPUS:78649863855

SN - 3642157629

SN - 9783642157622

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

SP - 344

EP - 358

BT - Distributed Computing - 24th International Symposium, DISC 2010, Proceedings

ER -