The algebraic degree of geometric optimization problems
Discrete & Computational Geometry
Algebraic optimization: the Fermat-Weber location problem
Mathematical Programming: Series A and B
Selecting distances in the plane
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Computational Geometry in C
Introduction to Algorithms
Fast approximations for sums of distances, clustering and the Fermat--Weber problem
Computational Geometry: Theory and Applications
Arrangements of Curves in the Plane - Topology, Combinatorics, and Algorithms
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Dynamic Additively Weighted Voronoi Diagrams in 2D
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
On coresets for k-means and k-median clustering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximating extent measures of points
Journal of the ACM (JACM)
Smaller coresets for k-median and k-means clustering
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
A PTAS for k-means clustering based on weak coresets
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
One-way and round-trip center location problems
Discrete Optimization
On the round-trip 1-center and 1-median problems
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
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In this paper we consider an extension of the classical facility location problem where besides n weighted customers, a set of p collection depots are also given. In this setting the service of a customer consists of the travel of a server to the customer and return back to the center via a collection depot. We have analyzed the problem and showed that the collection depots problem using the Euclidean metric can be transformed to O(p^2n^2) number of different classical facility location problems and this bound is tight. We then show the existence of small coresets for these problems. These coresets are then used to provide (1+@e)-factor approximation algorithms which have linear running times for fixed customer weights and @e.