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 - 2005/1/1

Y1 - 2005/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=26844449888&partnerID=8YFLogxK

U2 - 10.1007/11534273_18

DO - 10.1007/11534273_18

M3 - Conference article

AN - SCOPUS:26844449888

SN - 0302-9743

VL - 3608

SP - 195

EP - 204

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

T2 - 9th International Workshop on Algorithms and Data Structures, WADS 2005

Y2 - 15 August 2005 through 17 August 2005

ER -