Round-Trip Voronoi Diagrams and Doubling Density in Geographic Networks

Details Round-Trip Voronoi Diagrams and Doubling Density in Geographic Networks Round-Trip Voronoi Diagrams and Doubling Density in Geographic Networks

2010-05-06

arxiv.org/abs/1005.1053v1

Computer Science

Data Structures and Algorithms

21 pages, 7 figures. To appear in ISVD 2010.

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Round-Trip Voronoi Diagrams and Doubling Density in Geographic Networks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Round-Trip Voronoi Diagrams and Doubling Density in Geographic Networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Round-Trip Voronoi Diagrams and Doubling Density in Geographic Networks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-26744