Abstract
Given a geographic network G (e.g. road network, utility distribution grid) and a set of sites (e.g. post offices, fire stations), a two-site Voronoi diagram labels each vertex v ∈ G with the pair of sites that minimizes some distance function. The sum function defines the “distance” from v to a pair of sites s,t as the sum of the distances from v to each site. The round-trip function defines the “distance” as the minimum length tour starting and ending at v and visiting both s and t. A two-color variant begins with two different types of sites and labels each vertex with the minimum pair of sites of different types. In this paper, we provide new properties and algorithms for two-site and two-color Voronoi diagrams for these distance functions in a geographic network, including experimental results on the doubling distance of various point-of-interest sites. We extend some of these results to multi-color variants.
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Dickerson, M.T., Goodrich, M.T., Dickerson, T.D., Zhuo, Y.D. (2011). Round-Trip Voronoi Diagrams and Doubling Density in Geographic Networks. In: Gavrilova, M.L., Tan, C.J.K., Mostafavi, M.A. (eds) Transactions on Computational Science XIV. Lecture Notes in Computer Science, vol 6970. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25249-5_9
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