Approximating the geometric minimum-diameter spanning tree.

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

Approximating the geometric minimum-diameter spanning tree.

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

Research output: Contribution to conference › Paper › peer-review

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. In this paper, we present an approximation algorithm that generates a tree whose diameter is no more than (1 +) times that of a GMDST, for any > 0. Our algorithm reduces the problem to several grid-aligned versions of the problem and runs within time O(−3 + n) and space O(n) improving the result by Gudmundsson et al. [4].

Original language	English
Pages	1-4
Number of pages	4
State	Published - 1 Jan 2003
Event	CCCG 2003, Halifax - Nova Scotia, United States Duration: 11 Aug 2003 → 13 Aug 2003

Conference

Conference	CCCG 2003, Halifax
Country/Territory	United States
City	Nova Scotia
Period	11/08/03 → 13/08/03

Cite this

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title = "Approximating the geometric minimum-diameter spanning tree.",

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. In this paper, we present an approximation algorithm that generates a tree whose diameter is no more than (1 +) times that of a GMDST, for any > 0. Our algorithm reduces the problem to several grid-aligned versions of the problem and runs within time O(−3 + n) and space O(n) improving the result by Gudmundsson et al. [4].",

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T1 - Approximating the geometric minimum-diameter spanning tree.

AU - Spriggs, Michael

AU - Keil, J.

AU - Bespamyatnikh, Sergei

AU - Segal, Michael

AU - Snoeyink, Jack

PY - 2003/1/1

Y1 - 2003/1/1

N2 - 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. In this paper, we present an approximation algorithm that generates a tree whose diameter is no more than (1 +) times that of a GMDST, for any > 0. Our algorithm reduces the problem to several grid-aligned versions of the problem and runs within time O(−3 + n) and space O(n) improving the result by Gudmundsson et al. [4].

AB - 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. In this paper, we present an approximation algorithm that generates a tree whose diameter is no more than (1 +) times that of a GMDST, for any > 0. Our algorithm reduces the problem to several grid-aligned versions of the problem and runs within time O(−3 + n) and space O(n) improving the result by Gudmundsson et al. [4].

M3 - Paper

SP - 1

EP - 4

T2 - CCCG 2003, Halifax

Y2 - 11 August 2003 through 13 August 2003

ER -

Approximating the geometric minimum-diameter spanning tree.

Abstract

Conference

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