The minimum-area spanning tree problem

Paz Carmi, Matthew J. Katz, Joseph S.B. Mitchell

Research output: Contribution to journalConference articlepeer-review

3 Scopus citations


Motivated by optimization problems in sensor coverage, we formulate and study the Minimum-Area Spanning Tree (MAST) problem: Given a set P of n points in the plane, find a spanning tree of P of minimum "area," where the area of a spanning tree T is the area of the union of the n - 1 disks whose diameters are the edges in T. We prove that the Euclidean minimum spanning tree of P is a constant-factor approximation for MAST. We then apply this result to obtain constant-factor approximations for the Minimum-Area Range Assignment (MARA) problem, for the Minimum-Area Connected Disk Graph (MACDG) problem, and for the Minimum-Area Tour (MAT) problem. The first problem is a variant of the power assignment problem in radio networks, the second problem is a related natural problem, and the third problem is a variant of the traveling salesman problem.

Original languageEnglish
Pages (from-to)195-204
Number of pages10
JournalLecture Notes in Computer Science
StatePublished - 1 Jan 2005
Event9th International Workshop on Algorithms and Data Structures, WADS 2005 - Waterloo, Canada
Duration: 15 Aug 200517 Aug 2005

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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