An improved algorithm for constructing kth-order voronoi diagrams
IEEE Transactions on Computers
A faster approximation algorithm for the Steiner problem in graphs
Information Processing Letters
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Quickest paths, straight skeletons, and the city Voronoi diagram
Proceedings of the eighteenth annual symposium on Computational geometry
Introduction to Algorithms
Discrete Applied Mathematics
Voronoi Diagram for services neighboring a highway
Information Processing Letters
Proceedings of the 2006 ACM symposium on Applied computing
K nearest neighbor search in navigation systems
Mobile Information Systems
On k-Nearest Neighbor Voronoi Diagrams in the Plane
IEEE Transactions on Computers
Voronoi-based K nearest neighbor search for spatial network databases
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
Approximate order-k Voronoi cells over positional streams
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
Two-site Voronoi diagrams in geographic networks
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
Algorithm Design: Foundations, Analysis and Internet Examples
Algorithm Design: Foundations, Analysis and Internet Examples
Shortest paths and voronoi diagrams with transportation networks under general distances
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Voronoi diagrams with a transportation network on the euclidean plane
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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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.