Computational geometry: an introduction
Computational geometry: an introduction
Hierarchical Data Structures and Algorithms for Computer Graphics. Part I.
IEEE Computer Graphics and Applications
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Computers and Operations Research
An Optimization Based Heuristic for Political Districting
Management Science
Approximate Gaussian distributions in optimization by random perturbation methods
Selected papers of the second Panamerican workshop on Applied and computational mathematics
`` Direct Search'' Solution of Numerical and Statistical Problems
Journal of the ACM (JACM)
A continuous approach to the design of physical distribution systems
Computers and Operations Research
A simulated annealing approach to police district design
Computers and Operations Research - Location analysis
Locating stations on rapid transit lines
Computers and Operations Research - Location analysis
Computers and Industrial Engineering - Supply chain management
A multiplicatively-weighted Voronoi diagram approach to logistics districting
Computers and Operations Research
Solving the constrained p-center problem using heuristic algorithms
Applied Soft Computing
iRedistrict: Geovisual analytics for redistricting optimization
Journal of Visual Languages and Computing
| Hi-index | 0.01 |
Facility location problems are frequent in OR literature. In districting problems, on the other hand, the aim is to partition a territory into smaller units, called districts or zones, while an objective function is optimized and some constraints are satisfied, such as balance, contiguity, and compactness. Although many location and districting problems have been treated by assuming the region previously partitioned into a large number of elemental areas and further aggregating these units into districts with the aid of a mathematical programming model, continuous approximation, on the other hand, is based on the spatial density of demand, rather than on precise information on every elementary unit. Voronoi diagrams can be successfully used in association with continuous approximation models to solve location-districting problems, specially transportation and logistics applications. We discuss in the paper the context in which approximation algorithms can be used to solve this kind of problem.