Sparse geometric graphs with small dilation

Boris Aronov*, Mark De Berg, Otfried Cheong, Joachim Gudmundsson, Herman Haverkort, Antoine Vigneron

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

8 Scopus citations


Given a set S of n points in the plane, and an integer k such that 0 ≤ k < n, we show that a geometric graph with vertex set S, at most n - 1 + k edges, and dilation O(n/(k + 1)) can be computed in time O(n log n). We also construct n-point sets for which any geometric graph with n - 1 + k edges has dilation Ω(n/(k + 1)); a slightly weaker statement holds if the points of S are required to be in convex position.

Original languageEnglish (US)
Title of host publicationAlgorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings
Number of pages10
StatePublished - 2005
Externally publishedYes
Event16th International Symposium on Algorithms and Computation, ISAAC 2005 - Hainan, China
Duration: Dec 19 2005Dec 21 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3827 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other16th International Symposium on Algorithms and Computation, ISAAC 2005

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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