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

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

doi:10.1007/s00453-003-1056-z

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 journal › Article › peer-review

13 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 language	English
Pages (from-to)	577-589
Number of pages	13
Journal	Algorithmica
Volume	38
Issue number	4
DOIs	https://doi.org/10.1007/s00453-003-1056-z
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

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10.1007/s00453-003-1056-z

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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).",

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AU - Snoeyink, Jack

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

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Keywords

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