The minimum area spanning tree problem

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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 languageEnglish
Title of host publication Proceedings of the 21st European Workshop on Computational Geometry, Eindhoven, The Netherlands, March 9-11, 2005
PublisherTechnische Universiteit Eindhoven
Pages191-194
Number of pages4
StatePublished - 2005

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