Computing a (1+ε)-approximate geometric minimum-diameter spanning tree

Michael J. Spriggs, J. Mark Keil, Sergei Bespamyatnikh, Michael Segal, Jack Snoeyink

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Given a set P of points in the plane, a geometric minimum-diameter spanning tree (GMDST) of P is a spanning tree of P such that the longest path through the tree is minimized. For several years, the best upper bound on the time to compute a GMDST was cubic with respect to the number of points in the input set. Recently, Timothy Chan introduced a subcubic time algorithm. In this paper we present an algorithm that generates a tree whose diameter is no more than (1 + ε) times that of a GMDST, for any ε > 0. Our algorithm reduces the problem to several grid-aligned versions of the problem and runs within time O(ε-3+ n) and space O(n).

Original languageEnglish
Pages (from-to)577-589
Number of pages13
JournalAlgorithmica
Volume38
Issue number4
DOIs
StatePublished - 1 Jan 2004

Keywords

  • Approximation algorithm
  • Geometric graph
  • Minimum diameter spanning tree

ASJC Scopus subject areas

  • General Computer Science
  • Computer Science Applications
  • Applied Mathematics

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