Half-Space Proximal: A New Local Test for Extracting a Bounded Dilation Spanner of a Unit Disk Graph

  • Edgar Chavez
  • Stefan Dobrev
  • Evangelos Kranakis
  • Jaroslav Opatrny
  • Ladislav Stacho
  • Héctor Tejeda
  • Jorge Urrutia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3974)


We give a new local test, called a Half-Space Proximal or HSP test, for extracting a sparse directed or undirected subgraph of a given unit disk graph. The HSP neighbors of each vertex are unique, given a fixed underlying unit disk graph. The HSP test is a fully distributed, computationally simple algorithm that is applied independently to each vertex of a unit disk graph. The directed spanner obtained by this test is shown to be strongly connected, has out-degree at most six, its dilation is at most 2π+1, contains the minimum weight spanning tree as its subgraph and, unlike the Yao graph, it is rotation invariant. Since no coordinate assumption is needed to determine the HSP nodes, the test can be applied in any metric space.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Edgar Chavez
    • 1
  • Stefan Dobrev
    • 2
  • Evangelos Kranakis
    • 3
  • Jaroslav Opatrny
    • 4
  • Ladislav Stacho
    • 5
  • Héctor Tejeda
    • 1
  • Jorge Urrutia
    • 6
  1. 1.Escuela de Ciencias Físico-Matemáticas de la Universidad Michoacana. Partially supported by CONACyT grant 36911-AMéxico
  2. 2.School of Information Technology and Engineering (SITE)University of OttawaOttawa, OntarioCanada
  3. 3.School of Computer ScienceCarleton University, Ottawa. Research supported in part by NSERC and MITACSCanada
  4. 4.Department of Computer ScienceConcordia University, Montréal. Research supported in part by NSERCCanada
  5. 5.Department of MathematicsSimon Fraser UniversityBurnaby, British ColumbiaCanada
  6. 6.Instituto de MatemáticasUniversidad Nacional Autónoma de México. Research partially supported by CONACYT grant no. 37540-A, and PAPIIT UNAMMexico

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