A primal-dual algorithm for minimizing a sum of Euclidean norms
Journal of Computational and Applied Mathematics
Computing the Shortest Network under a Fixed Topology
IEEE Transactions on Computers
Comparison of Two Kinds of Prediction-Correction Methods for Monotone Variational Inequalities
Computational Optimization and Applications
Semidefinite programming for ad hoc wireless sensor network localization
Proceedings of the 3rd international symposium on Information processing in sensor networks
Efficient Algorithms for the Smallest Enclosing Ball Problem
Computational Optimization and Applications
An Improved Extra-Gradient Method for Minimizing a Sum of p-norms--A Variational Inequality Approach
Computational Optimization and Applications
Semidefinite programming based algorithms for sensor network localization
ACM Transactions on Sensor Networks (TOSN)
A Newton's method for perturbed second-order cone programs
Computational Optimization and Applications
The Q method for second order cone programming
Computers and Operations Research
Traffic-aware relay node deployment for data collection in wireless sensor networks
SECON'09 Proceedings of the 6th Annual IEEE communications society conference on Sensor, Mesh and Ad Hoc Communications and Networks
An entropy regularization technique for minimizing a sum of Tchebycheff norms
Applied Numerical Mathematics
Journal of Global Optimization
Computational Optimization and Applications
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In recent years rich theories on polynomial-time interior-point algorithms have been developed. These theories and algorithms can be applied to many nonlinear optimization problems to yield better complexity results for various applications. In this paper, the problem of minimizing a sum of Euclidean norms is studied. This problem is convex but not everywhere differentiable. By transforming the problem into a standard convex programming problem in conic form, we show that an $\epsilon$-optimal solution can be computed efficiently using interior-point algorithms. As applications to this problem, polynomial-time algorithms are derived for the Euclidean single facility location problem, the Euclidean multifacility location problem, and the shortest network under a given tree topology. In particular, by solving the Newton equation in linear time using {\em Gaussian elimination on leaves of a tree}, we present an algorithm which computes an $\epsilon$-optimal solution to the shortest network under a given full Steiner topology interconnecting N regular points, in $O(N \sqrt{N}(\log(\bar c/\epsilon)+\log N))$ arithmetic operations where $\bar c$ is the largest pairwise distance among the given points. The previous best-known result on this problem is a graphical algorithm which requires O(N2) arithmetic operations under certain conditions.