The maximal number of pairwise communicating stations under limitations of maximal and minimal communication distance

Lance Drager, Jeffrey Lee, Clyde Martin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the problem of determining the maximal number of stations that can maintain a total network of communication. We assume that there is a distance R which is that maximal distance that two stations can be separated and remain in contact. We also assume that there is a distance r which is them minimal separation that allows communication. This problem is intimately related to the problem of packing disks within a circle. The problem of finding the circle of smallest radius enclosing a finite set of points in the plane arises in a number of applications. Many numerical codes have been written for this problem. We provide a framework for investigating the geometric properties of this circle that may be useful in the theoretical analysis of applications. We show that a circle C enclosing a finite set of points P is the minimal circle if and only if it is rigid in the sense that it cannot be translated while still enclosing P. We use this result to find a sharp estimate on the diameter of the minimal circle in terms of the diameter of P. We also show that the center of the minimal circle is contained in the convex hull of P.

Original languageEnglish
Title of host publicationProceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Pages5334-5340
Number of pages7
DOIs
StatePublished - 2007
Event46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States
Duration: Dec 12 2007Dec 14 2007

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Conference

Conference46th IEEE Conference on Decision and Control 2007, CDC
CountryUnited States
CityNew Orleans, LA
Period12/12/0712/14/07

Keywords

  • Communication
  • Convex optimization
  • Minimal circle
  • Spanning circle

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  • Cite this

    Drager, L., Lee, J., & Martin, C. (2007). The maximal number of pairwise communicating stations under limitations of maximal and minimal communication distance. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC (pp. 5334-5340). [4434332] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2007.4434332