Performance Guarantees for Approximation Algorithms Depending on Parametrized Triangle Inequalities
SIAM Journal on Discrete Mathematics
Performance guarantees for the TSP with a parameterized triangle inequality
Information Processing Letters
Introduction to Algorithms
Power Consumption in Packet Radio Networks (Extended Abstract)
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
On the History of the Minimum Spanning Tree Problem
IEEE Annals of the History of Computing
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Motivated by optimization problems in sensor coverage, we formulate and study the Minimum-Area Spanning Tree (mast) problem: Given a set $\mathcal{P}$ of n points in the plane, find a spanning tree of $\mathcal{P}$ of minimum “area,” where the area of a spanning tree $\mathcal{T}$ is the area of the union of the n–1 disks whose diameters are the edges in $\mathcal{T}$. We prove that the Euclidean minimum spanning tree of $\mathcal{P}$ 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.