Computing the greedy spanner in near-quadratic time

Prosenjit Bose, Paz Carmi, Mohammad Farshi, Anil Maheshwari, Michiel Smid

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

The greedy algorithm produces high-quality spanners and, therefore, is used in several applications. However, even for points in d-dimensional Euclidean space, the greedy algorithm has near-cubic running time. In this paper, we present an algorithm that computes the greedy spanner for a set of n points in a metric space with bounded doubling dimension in O(n 2log n) time. Since computing the greedy spanner has an Ω(n 2) lower bound, the time complexity of our algorithm is optimal within a logarithmic factor.

Original languageEnglish
Pages (from-to)711-729
Number of pages19
JournalAlgorithmica
Volume58
Issue number3
DOIs
StatePublished - 1 Nov 2010
Externally publishedYes

Keywords

  • Dilation
  • Doubling dimension
  • Greedy algorithm
  • Spanner
  • Stretch factor

ASJC Scopus subject areas

  • Computer Science (all)
  • Computer Science Applications
  • Applied Mathematics

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