Localization and routing in sensor networks by local angle information

Jehoshua Bruck, Jie Gao, Anxiao Jiang

Research output: Contribution to conferencePaperpeer-review

78 Scopus citations


Location information is very useful in the design of sensor network infrastructures. In this paper, we study the anchor-free 2D localization problem by using local angle measurements in a sensor network. We prove that given a unit disk graph and the angles between adjacent edges, it is NP-hard to find a valid embedding in the plane such that neighboring nodes are within distance 1 from each other and non-neighboring nodes are at least distance 1 away. Despite the negative results, however, one can find a planar spanner of a unit disk graph by using only local angles. The planar spanner can be used to generate a set of virtual coordinates that enable efficient and local routing schemes such as geographical routing or approximate shortest path routing. We also proposed a practical anchor-free embedding scheme by solving a linear program. We show by simulation that not only does it give very good local embedding, i.e., neighboring nodes are close and non-neighboring nodes are far away, but it also gives a quite accurate global view such that geographical routing and approximate shortest path routing on the embedded graph are almost identical to those on the original (true) embedding. The embedding algorithm can be adapted to other models of wireless sensor networks and is robust to measurement noise.

Original languageEnglish (US)
Number of pages12
StatePublished - 2005
Externally publishedYes
EventMOBIHOC 2005: 6th ACM International Symposium on Mobile Ad Hoc Networking and Computing - Urbana-Champaign, IL, United States
Duration: May 25 2005May 28 2005


OtherMOBIHOC 2005: 6th ACM International Symposium on Mobile Ad Hoc Networking and Computing
Country/TerritoryUnited States
CityUrbana-Champaign, IL

All Science Journal Classification (ASJC) codes

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications


  • Embedding
  • Geographical routing
  • Localization
  • Planar spanner subgraph
  • Sensor networks
  • Wireless networks


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