SINR Diagrams: Convexity and its applications in wireless networks

Chen Avin, Yuval Emek, Erez Kantor, Zvi Lotker, David Peleg, Liam Roditty

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


The rules governing the availability and quality of connections in a wireless network are described by physical models such as the signal-to-interference & noise ratio (SINR) model. For a collection of simultaneously transmitting stations in the plane, it is possible to identify a reception zone for each station, consisting of the points where its transmission is received correctly. The resulting SINR diagram partitions the plane into a reception zone per station and the remaining plane where no station can be heard. SINR diagrams appear to be fundamental to understanding the behavior of wireless networks, and may play a key role in the development of suitable algorithms for such networks, analogous perhaps to the role played by Voronoi diagrams in the study of proximity queries and related issues in computational geometry. So far, however, the properties of SINR diagrams have not been studied systematically, and most algorithmic studies in wireless networking rely on simplified graph-based models such as the unit disk graph (UDG) model, which conveniently abstract away interference-related complications, and make it easier to handle algorithmic issues, but consequently fail to capture accurately some important aspects of wireless networks. This article focuses on obtaining some basic understanding of SINR diagrams, their properties and their usability in algorithmic applications. Specifically, we have shown that assuming uniform power transmissions, the reception zones are convex and relatively well-rounded. These results are then used to develop an efficient approximation algorithm for a fundamental point location problem in wireless networks.

Original languageEnglish
Article number18
JournalJournal of the ACM
Issue number4
StatePublished - 1 Aug 2012


  • Computational geometry
  • Convexity
  • Point location
  • Polynomials
  • SINR diagrams
  • Voronoi diagrams
  • Wireless networks

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Information Systems
  • Hardware and Architecture
  • Artificial Intelligence


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