DocumentCode :
3173091
Title :
Round-Trip Voronoi Diagrams and Doubling Density in Geographic Networks
Author :
Dickerson, Matthew T. ; Goodrich, Michael T. ; Dickerson, Thomas D.
Author_Institution :
Dept. of Comput. Sci., Middlebury Coll., Middlebury, VT, USA
fYear :
2010
fDate :
28-30 June 2010
Firstpage :
132
Lastpage :
141
Abstract :
The round-trip distance function on a geographic network (such as a road network, flight network, or utility distribution grid) defines the "distance" from a single vertex to a pair of vertices as the minimum length tour visiting all three vertices and ending at the starting vertex. Given a geographic network and a subset of its vertices called "sites" (for example a road network with a list of grocery stores), a two-site round-trip Voronoi diagram labels each vertex in the network with the pair of sites that minimizes the round-trip distance from that vertex. Alternatively, given a geographic network and two sets of sites of different types (for example grocery stores and coffee shops), a two-color round-trip Voronoi diagram labels each vertex with the pair of sites of different types minimizing the round-trip distance. In this paper, we prove several new properties of two-site and two-color round-trip Voronoi diagrams in a geographic network, including a relationship between the "doubling density" of sites and an upper bound on the number of non-empty Voronoi regions. We show how those lemmas can be used in new algorithms asymptotically more efficient than previous known algorithms when the networks have reasonable distribution properties related to doubling density, and we provide experimental data suggesting that road networks with standard point-of-interest sites have these properties.
Keywords :
computational geometry; graph theory; minimisation; doubling density relationship; flight network; geographic networks; network vertices; nonempty Voronoi regions; road network; round-trip Voronoi diagrams; round-trip distance minimization; utility distribution grid; Computer science; Costs; Educational institutions; Fires; Hospitals; Labeling; Roads; Transportation; Upper bound;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Voronoi Diagrams in Science and Engineering (ISVD), 2010 International Symposium on
Conference_Location :
Quebec, QC
Print_ISBN :
978-1-4244-7606-0
Electronic_ISBN :
978-1-4244-7605-3
Type :
conf
DOI :
10.1109/ISVD.2010.29
Filename :
5521418
Link To Document :
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