TY - JOUR

T1 - The minimum-area spanning tree problem

AU - Carmi, Paz

AU - Katz, Matthew J.

AU - Mitchell, Joseph S.B.

N1 - Funding Information:
* Corresponding author. E-mail addresses: [email protected] (P. Carmi), [email protected] (M.J. Katz), [email protected] (J.S.B. Mitchell). 1 Partially supported by a Kreitman Foundation doctoral fellowship, and by the Lynn and William Frankel Center for Computer Sciences. 2 Partially supported by grant No. 2000160 from the US–Israel Binational Science Foundation. 3 Partially supported by grant No. 2000160 from the US–Israel Binational Science Foundation, NASA Ames Research (NAG2-1620), the National Science Foundation (CCR-0098172, ACI-0328930, CCF-0431030, CCF-0528209), and Metron Aviation.

PY - 2006/10/1

Y1 - 2006/10/1

N2 - 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.

AB - 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.

KW - Approximation algorithms

KW - Disk graphs

KW - Geometric optimization

KW - Minimum spanning tree

KW - Range assignment

KW - Traveling salesperson problem

UR - http://www.scopus.com/inward/record.url?scp=84867958392&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2006.03.001

DO - 10.1016/j.comgeo.2006.03.001

M3 - Article

AN - SCOPUS:84867958392

SN - 0925-7721

VL - 35

SP - 218

EP - 225

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

IS - 3

ER -