Computing a (1+ε)-Approximate Geometric Minimum-Diameter Spanning Tree Authors
First Online: 05 December 2003 Received: 23 January 2002 Revised: 26 July 2003 DOI:
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
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 tree Approximation algorithm Geometric graph References
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