Half-space proximal: a new local test for extracting a bounded dilation spanner of a unit disk graph

  • Authors:

  • Edgar Chavez;Stefan Dobrev;Evangelos Kranakis;Jaroslav Opatrny;Ladislav Stacho;Héctor Tejeda;Jorge Urrutia

  • Affiliations:

  • Escuela de Ciencias Físico-Matemáticas de la Universidad Michoacana. Partially supported by CONACyT grant 36911-A, México;School of Information Technology and Engineering (SITE), University of Ottawa, Ottawa, Ontario, Canada;School of Computer Science, Carleton University, Ottawa. Research supported in part by NSERC and MITACS;Department of Computer Science, Concordia University, Montréal. Research supported in part by NSERC;Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada;Escuela de Ciencias Físico-Matemáticas de la Universidad Michoacana. Partially supported by CONACyT grant 36911-A, México;Instituto de Matemáticas, Universidad Nacional Autónoma de México. Research partially supported by CONACYT grant no. 37540-A, and PAPIIT UNAM

  • Venue:
  • OPODIS'05 Proceedings of the 9th international conference on Principles of Distributed Systems
  • Year:
  • 2005

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Abstract

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.