Optimally Solving a Transportation Problem Using Voronoi Diagrams

  title={Optimally Solving a Transportation Problem Using Voronoi Diagrams},
  author={Darius Gei\ss and Rolf Klein and Rainer Penninger},
We consider the following variant of the well-known Monge-Kantorovich transportation problem. Let S be a set of n point sites in R. A bounded set C ⊂ R is to be distributed among the sites p ∈ S such that (i), each p receives a subset Cp of prescribed volume and (ii), the average distance of all points z of C from their respective sites p is minimized. In our model, volume is quantified by a measure μ, and the distance between a site p and a point z is given by a function dp(z). Under quite… CONTINUE READING

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Optimally solving a transportation problem using Voronoi diagrams

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