Unit disk graph and physical interference model: Putting pieces together

Emmanuelle Lebhar, Zvi Lotker

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

41 Scopus citations

Abstract

Modeling communications in wireless networks is a challenging task, since it requires a simple mathematical object on which efficient algorithms can be designed but which must also reflect the complex physical constraints inherent in wireless networks, such as interferences, the lack of global knowledge, and purely local computations. As a tractable mathematical object, the unit disk graph (UDG) is a popular model that has enabled the development of efficient algorithms for crucial networking problems. In a p-UDG, two nodes are connected if and only if their distance is at most p, for some p > 0. However, such a connectivity requirement is basically not compatible with the reality of wireless networks due to the environment of the nodes as well as the constraints of radio transmission. For this purpose, the signal interference plus noise ratio model (SINR) is the more commonly used model. The SINR model focuses on radio interferences created over the network depending on the distance to transmitters. Nevertheless, due to its complexity, this latter model has been the subject of very few theoretical investigations and lacks of good algorithmic features. In this paper, we demonstrate how careful scheduling of the nodes enables the two models to be combined to give the benefits of both the algorithmic features of the UDG and the physical validity of the SINR. Precisely, we show that it is possible to emulate a 1/√n ln n-UDG that satisfies the constraints of the SINR over any set of n wireless nodes distributed uniformly in a unit square, with only a O(ln3 n) time and power stretch factor. The main strength of our contribution lies in the fact that the scheduling is set in a fully distributed way and considers non-uniform power ranges, and it can therefore fit the sensor network setting. Moreover, our scheduling is optimal up to a polylogarithmic factor in terms of throughput capacity according to the lower bound of Gupta and Kumar.

Original languageEnglish
Title of host publicationIPDPS 2009 - Proceedings of the 2009 IEEE International Parallel and Distributed Processing Symposium
DOIs
StatePublished - 26 Nov 2009
Event23rd IEEE International Parallel and Distributed Processing Symposium, IPDPS 2009 - Rome, Italy
Duration: 23 May 200929 May 2009

Publication series

NameIPDPS 2009 - Proceedings of the 2009 IEEE International Parallel and Distributed Processing Symposium

Conference

Conference23rd IEEE International Parallel and Distributed Processing Symposium, IPDPS 2009
Country/TerritoryItaly
CityRome
Period23/05/0929/05/09

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Hardware and Architecture
  • Software

Fingerprint

Dive into the research topics of 'Unit disk graph and physical interference model: Putting pieces together'. Together they form a unique fingerprint.

Cite this