Minimum-cost load-balancing partitions
Proceedings of the twenty-second annual symposium on Computational geometry
Median and related local filters for tensor-valued images
Signal Processing
Optimal Free-Space Management and Routing-Conscious Dynamic Placement for Reconfigurable Devices
IEEE Transactions on Computers
The projection median of a set of points
Computational Geometry: Theory and Applications
A continuous analysis framework for the solution of location-allocation problems with dense demand
Computers and Operations Research
Impact of the Norm on Optimal Locations
ICCSA '09 Proceedings of the International Conference on Computational Science and Its Applications: Part I
Finding a Hausdorff Core of a Polygon: On Convex Polygon Containment with Bounded Hausdorff Distance
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Integer point sets minimizing average pairwise L1 distance: What is the optimal shape of a town?
Computational Geometry: Theory and Applications
Extended grassfire transform on medial axes of 2D shapes
Computer-Aided Design
Matrix-valued filters as convex programs
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
On vehicle placement to intercept moving targets
Automatica (Journal of IFAC)
Dividing a Territory Among Several Facilities
INFORMS Journal on Computing
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We give the firstexact algorithmic study of facility location problems that deal with finding a median for acontinuum of demand points. In particular, we consider versions of the "continuousk-median (Fermat-Weber) problem" where the goal is to select one or more center points that minimize the average distance to a set of points in a demandregion. In such problems, the average is computed as an integral over the relevant region, versus the usual discrete sum of distances. The resulting facility location problems are inherently geometric, requiring analysis techniques of computational geometry. We provide polynomial-time algorithms for various versions of theL1 1-median (Fermat-Weber) problem. We also consider the multiple-center version of theL1k-median problem, which we prove is NP-hard for largek.