The minimum-area spanning tree problem

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

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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)218-225
Number of pages8
JournalComputational Geometry: Theory and Applications
Volume35
Issue number3
DOIs
StatePublished - 1 Oct 2006

Keywords

  • Approximation algorithms
  • Disk graphs
  • Geometric optimization
  • Minimum spanning tree
  • Range assignment
  • Traveling salesperson problem

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