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Published in:
2011 | OriginalPaper | Chapter
Round-Trip Voronoi Diagrams and Doubling Density in Geographic Networks
Authors : Matthew T. Dickerson, Michael T. Goodrich, Thomas D. Dickerson, Ying Daisy Zhuo
Published in: Transactions on Computational Science XIV
Publisher: Springer Berlin Heidelberg
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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.