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### Round-Tour Voronoi Diagrams

Hidenori Fujii, Kokichi Sugihara
2009 2009 Sixth International Symposium on Voronoi Diagrams
We call this partitioning a "round-tour Voronoi Diagram" for the restaurants and bookstores.  ...  Abstract-This paper proposes a new generalization of the Voronoi diagram.  ...  Figure 6 6 shows an example of a round-tour Voronoi diagram with O(n 2 ) Voronoi regions for |A| = |B| = n. Fig. 6 . 6 Round-tour Voronoi diagram with O(n 2 ) Voronoi regions.  ...

### Round-Trip Voronoi Diagrams and Doubling Density in Geographic Networks [article]

Matthew T. Dickerson, Michael T. Goodrich, Thomas D. Dickerson
2010 arXiv   pre-print
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  ...  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  ...  Round-Trip Voronoi Diagram Algorithms We now provide algorithms to compute the round-trip function Voronoi diagram for a geographic network and set of sites G = (V, K, E).  ...

### Intersections with random geometric objects

Prosenjit Bose, Luc Devroye
1998 Computational geometry
Using this result, we explore the intersection complexity of a random Voronoi diagram with the following target objects which may or may not be random: a line segment, a Voronoi diagram, a minimum spanning  ...  We first study the expected size of the intersection between a random Voronoi diagram and a generic geometric object that consists of a finite collection of line segments in the plane.  ...  We are interested in the (random) number of intersections between a random Voronoi diagram and certain other objects, such as line segments, spheres, grids, minimal spanning trees, traveling salesman tours  ...

### Adaptive Deployment of Mobile Robotic Networks

Jerome Le Ny, George J. Pappas
2013 IEEE Transactions on Automatic Control
In particular, if , then the generalized Voronoi diagram becomes a power diagram.  ...  In particular for , the generalized Voronoi diagram is called a power diagram [30] , [31] , and the generalized Voronoi cell a power cell.  ...

### Representation of Imprecise Digital Objects [chapter]

Isabelle Sivignon
2016 Lecture Notes in Computer Science
The additivelymultplicatively distance is associated with the so-called compoundly-weighted Voronoi diagram [14] , which falls in the class of non-linear Voronoi diagrams (bissectors are not linear).  ...  With such a setting, we may build on well-known results on the Voronoi Diagram stability through growth process.  ...

### Fast Parallel Algorithms for Euclidean Minimum Spanning Tree and Hierarchical Spatial Clustering [article]

Yiqiu Wang, Shangdi Yu, Yan Gu, Julian Shun
2021 arXiv   pre-print
This ordinary Voronoi diagram divides the Voronoi cell into multiple subcells, each of which corresponds to a cell in the Voronoi diagram of one higher order.  ...  Theorder Voronoi Diagram is a generalization of the ordinary Voronoi diagram, where points in each cell share the same -nearest neighbors [9] .  ...

### New Algorithms Based on the Voronoi Diagram Applied in a Pilot Study on Normal Mucosa and Carcinomas

J. Sudbø, R. Marcelpoil, A. Reith
2000 Analytical Cellular Pathology
To assess a possible diagnostic and prognostic value of quantitiative tissue architecture analysis, structural features based on the Voronoi Diagram (VD) and its subgraphs were developed and tested.A series  ...  New algorithms based on the Voronoi Diagram applied in a pilot study on normal mucosa and carcinomas J. Sudbø a, * , R. Marcelpoil b and A.  ...  When we use this rule for every point considered, the area of interest is completely covered by adjacent polygons, constituting the Voronoi Diagram (VD).  ...

### ForestMaps: A Computational Model and Visualization for Forest Utilization [chapter]

Hannah Bast, Jonas Sternisko, Sabine Storandt
2014 Lecture Notes in Computer Science
Fig. 3 . 3 Left: a small artificial example of a street Voronoi diagram.  ...  From a geometric point of view, this amounts to computing a Voronoi diagram for all vertices and sum up the street lengths inside the respective Voronoi cells.  ...

### Good triangulations yield good tours

Adam N. Letchford, Nicholas A. Pearson
2008 Computers & Operations Research
Indeed, our experiments show that the resulting tours are on average within 0.1% of optimality.  ...  The points which are assigned to two vertices in V lie on line-segments, which define the Voronoi diagram [20] . The geometric dual of the Voronoi diagram is the Delaunay triangulation [21] .  ...  The Delaunay triangulation, and its dual graph, the Voronoi diagram, are well-known in computational geometry.  ...

### Computational geometry and computer graphics [chapter]

1993 Lecture Notes in Computer Science
The Delaunay triangulation and Voronoi diagrams are closely related. Edges of the Voronoi diagram create vertices that correspond to the triangles of the Delaunay triangulation.  ...  For example, the dotted lines in Figure 2 give the Voronoi diagram for the set of sites shown triangulated in Figure 1 . Voronoi diagrams can be used to solve various nearest neighbor problems.  ...

### Computational geometry and computer graphics

D.P. Dobkin
1992 Proceedings of the IEEE
The Delaunay triangulation and Voronoi diagrams are closely related. Edges of the Voronoi diagram create vertices that correspond to the triangles of the Delaunay triangulation.  ...  For example, the dotted lines in Figure 2 give the Voronoi diagram for the set of sites shown triangulated in Figure 1 . Voronoi diagrams can be used to solve various nearest neighbor problems.  ...

### Data-Gathering Scheme Using AUVs in Large-Scale Underwater Sensor Networks: A Multihop Approach

2016 Sensors
Figure 5 . 5 Acoustic Sensor Network with Voronoi regions. Figure 5 . 5 Acoustic Sensor Network with Voronoi regions. Figure 6 . 6 AUV operating mode transition diagram.  ...  Figure 6 . 6 AUV operating mode transition diagram. Figure 7 . 7 Events that may occur at a tour-point (a) AUV in mode-f (b) AUV in mode-r.  ...

### Multi-robot coordination through dynamic Voronoi partitioning for informative adaptive sampling in communication-constrained environments

Stephanie Kemna, John G. Rogers, Carlos Nieto-Granda, Stuart Young, Gaurav S. Sukhatme
2017 2017 IEEE International Conference on Robotics and Automation (ICRA)
We use an approach that combines Voronoi partitioning with  ...  We use a dynamic Voronoi partitioning approach whereby the vehicles, in a decentralized fashion, repeatedly calculate weighted Voronoi partitions for the space.  ...  Our approach is different from Bakolas and Tsiotras' 'dynamic Voronoi diagram' [15] , where a Voronoi partition is re-calculated given expected time to reach Voronoi centers, or 'terminal positions'.  ...

### Near optimal minimal convex hulls of disks

Josef Kallrath, Joonghyun Ryu, Chanyoung Song, Mokwon Lee, Deok-Soo Kim
2021 Journal of Global Optimization
Here we propose a polylithic framework of the problem for big problem instances by combining the following algorithms and models: (i) A fast disk-packing algorithm based on Voronoi diagrams, non-linear  ...  Fig. 12 12 Voronoi diagrams used in the proposed algorithm. a VD(P): The ordinary Voronoi diagram of a point set P. b VD(D): The Voronoi diagram of a disk set D. c VD(D, CC): The Voronoi diagram in a circular  ...  (l through o): from SET-D Voronoi diagram of a point set P in R 2 . VD(D) the Voronoi diagram of a circular disk set D in R 2 .  ...

### Distributed Multi-Actuator Control for Workload Balancing in Wireless Sensor and Actuator Networks

Changhua Wu, Girma S. Tewolde, Weihua Sheng, Bin Xu, Yu Wang
2011 IEEE Transactions on Automatic Control
We applied a simple partition method, Voronoi diagram [17] , where all points in the partition R i are closer to the position pi of ai than to positions of all other actuators.  ...  The proposed control method uses classical Voronoi diagram as the partition method to divide the network into k partitions and uses heuristic algorithms in the previous section to estimate each actuator's  ...
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