NDLI: Round-Trip Voronoi Diagrams and Doubling Density in Geographic Networks

Content Provider	IEEE Xplore Digital Library
Author	Dickerson, M.T. Goodrich, M.T. Dickerson, T.D.
Copyright Year	2010
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.
Starting Page	132
Ending Page	141
File Size	468683
Page Count	10
File Format	PDF
ISBN	9781424476060
e-ISBN	9781424476053
DOI	10.1109/ISVD.2010.29
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-06-28
Publisher Place	Canada
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Roads Educational institutions Computer science Upper bound Transportation Costs Hospitals Fires Labeling
Content Type	Text
Resource Type	Article

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