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 language | English |
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Pages (from-to) | 577-589 |
Number of pages | 13 |
Journal | Algorithmica |
Volume | 38 |
Issue number | 4 |
DOIs | |
State | Published - 1 Jan 2004 |
Keywords
- Approximation algorithm
- Geometric graph
- Minimum diameter spanning tree
ASJC Scopus subject areas
- General Computer Science
- Computer Science Applications
- Applied Mathematics