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 -