Connectivity guarantees for wireless networks with directional antennas

Paz Carmi, Matthew J. Katz, Zvi Lotker, Adi Rosén

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


We study a combinatorial geometric problem related to the design of wireless networks with directional antennas. Specifically, we are interested in necessary and sufficient conditions on such antennas that enable one to build a connected communication network, and in efficient algorithms for building such networks when possible. We formulate the problem by a set P of n points in the plane, indicating the positions of n transceivers. Each point is equipped with an α-degree directional antenna, and one needs to adjust the antennas (represented as wedges), by specifying their directions, so that the resulting (undirected) communication graph G is connected. (Two points p,qεP are connected by an edge in G, if and only if q lies in p's wedge and p lies in q's wedge.) We prove that if α=60°, then it is always possible to adjust the wedges so that G is connected, and that α≥60° is sometimes necessary to achieve this. Our proof is constructive and yields an O(nlogk) time algorithm for adjusting the wedges, where k is the size of the convex hull of P. Sometimes it is desirable that the communication graph G contain a Hamiltonian path. By a result of Fekete and Woeginger (1997) [8], if α=90°, then it is always possible to adjust the wedges so that G contains a Hamiltonian path. We give an alternative proof to this, which is interesting, since it produces paths of a different nature than those produced by the construction of Fekete and Woeginger. We also show that for any n and ε>0, there exist sets of points such that G cannot contain a Hamiltonian path if α=90°-ε.

Original languageEnglish
Pages (from-to)477-485
Number of pages9
JournalComputational Geometry: Theory and Applications
Issue number9
StatePublished - 1 Nov 2011


  • Connectivity
  • Directional antennas
  • Polygonal paths
  • Wireless networks

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics


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