The minimum area spanning tree problem

Paz Carmi; Matthew J. Katz

The minimum area spanning tree problem

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We define and study the Minimum Area Spanning Tree (MAST) problem. Given a set P of n points in the plane, find a spanning tree T of P of minimum area, where the area of a spanning tree is the area of the union of the n − 1 disks whose diameters are the edges in T . We prove that the minimum spanning tree of P is a constant-factor approximation for mast. We then apply this result to obtain a constant-factor approximation for the Minimum Area Range Assignment (MARA) problem and for the Minimum Area Connected Disk Graph (MACDG) problem. The former problem is a variant of the power assignment problem in radio networks, and the latter problem is a related natural problem

Original language	English
Title of host publication	Proceedings of the 21st European Workshop on Computational Geometry, Eindhoven, The Netherlands, March 9-11, 2005
Publisher	Technische Universiteit Eindhoven
Pages	191-194
Number of pages	4
State	Published - 2005

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Cite this

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title = "The minimum area spanning tree problem",

abstract = "We define and study the Minimum Area Spanning Tree (MAST) problem. Given a set P of n points in the plane, find a spanning tree T of P of minimum area, where the area of a spanning tree is the area of the union of the n − 1 disks whose diameters are the edges in T . We prove that the minimum spanning tree of P is a constant-factor approximation for mast. We then apply this result to obtain a constant-factor approximation for the Minimum Area Range Assignment (MARA) problem and for the Minimum Area Connected Disk Graph (MACDG) problem. The former problem is a variant of the power assignment problem in radio networks, and the latter problem is a related natural problem",

author = "Paz Carmi and Katz, \{Matthew J.\}",

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language = "English",

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booktitle = "Proceedings of the 21st European Workshop on Computational Geometry, Eindhoven, The Netherlands, March 9-11, 2005",

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T1 - The minimum area spanning tree problem

AU - Carmi, Paz

AU - Katz, Matthew J.

PY - 2005

Y1 - 2005

N2 - We define and study the Minimum Area Spanning Tree (MAST) problem. Given a set P of n points in the plane, find a spanning tree T of P of minimum area, where the area of a spanning tree is the area of the union of the n − 1 disks whose diameters are the edges in T . We prove that the minimum spanning tree of P is a constant-factor approximation for mast. We then apply this result to obtain a constant-factor approximation for the Minimum Area Range Assignment (MARA) problem and for the Minimum Area Connected Disk Graph (MACDG) problem. The former problem is a variant of the power assignment problem in radio networks, and the latter problem is a related natural problem

AB - We define and study the Minimum Area Spanning Tree (MAST) problem. Given a set P of n points in the plane, find a spanning tree T of P of minimum area, where the area of a spanning tree is the area of the union of the n − 1 disks whose diameters are the edges in T . We prove that the minimum spanning tree of P is a constant-factor approximation for mast. We then apply this result to obtain a constant-factor approximation for the Minimum Area Range Assignment (MARA) problem and for the Minimum Area Connected Disk Graph (MACDG) problem. The former problem is a variant of the power assignment problem in radio networks, and the latter problem is a related natural problem

M3 - Conference contribution

SP - 191

EP - 194

BT - Proceedings of the 21st European Workshop on Computational Geometry, Eindhoven, The Netherlands, March 9-11, 2005

PB - Technische Universiteit Eindhoven

ER -

The minimum area spanning tree problem

Abstract

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