Algorithmica

, Volume 38, Issue 4, pp 577–589

Computing a (1+ε)-Approximate Geometric Minimum-Diameter Spanning Tree

Article

DOI: 10.1007/s00453-003-1056-z

Cite this article as:
Spriggs, M., Keil, J., Bespamyatnikh, S. et al. Algorithmica (2004) 38: 577. doi:10.1007/s00453-003-1056-z

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).

Minimum diameter spanning treeApproximation algorithmGeometric graph

Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.School of Computer Science, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1Canada
  2. 2.Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan, S7N 5A9Canada
  3. 3.Department of Computer Science, Duke University, Box 90129, Durham, NC 27708USA
  4. 4.Communication Systems Engineering Department, Ben-Gurion University of the Negev, Beer-Sheva, 84105Israel
  5. 5.Department of Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3175USA