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Round-Tour Voronoi Diagrams
2009
2009 Sixth International Symposium on Voronoi Diagrams
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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. ...
doi:10.1109/isvd.2009.9
dblp:conf/isvd/FujiiS09
fatcat:koxcwh5mmrhkxjzg7jtykn7dwy
Round-Trip Voronoi Diagrams and Doubling Density in Geographic Networks
[article]
2010
arXiv
pre-print
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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). ...
arXiv:1005.1053v1
fatcat:7kgmdsg2b5biresnmp6ahvev5a
Intersections with random geometric objects
1998
Computational geometry
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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 ...
doi:10.1016/s0925-7721(98)00004-2
fatcat:fpbk62ycsbbd7ahj6hebtsfscm
Adaptive Deployment of Mobile Robotic Networks
2013
IEEE Transactions on Automatic Control
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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. ...
doi:10.1109/tac.2012.2215512
fatcat:t77tlr3ztjgwhbb7cdpkalom64
Representation of Imprecise Digital Objects
[chapter]
2016
Lecture Notes in Computer Science
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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. ...
doi:10.1007/978-3-319-32360-2_31
fatcat:ksztnmwcsrfurk746ooyp2rsge
Fast Parallel Algorithms for Euclidean Minimum Spanning Tree and Hierarchical Spatial Clustering
[article]
2021
arXiv
pre-print
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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] . ...
arXiv:2104.01126v1
fatcat:c3ocmhisqfcqrfpyudtfmqmhyi
New Algorithms Based on the Voronoi Diagram Applied in a Pilot Study on Normal Mucosa and Carcinomas
2000
Analytical Cellular Pathology
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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). ...
doi:10.1155/2000/389361
pmid:11310643
pmcid:PMC4618427
fatcat:avcagina2jayjp6mgsyponeq44
ForestMaps: A Computational Model and Visualization for Forest Utilization
[chapter]
2014
Lecture Notes in Computer Science
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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. ...
doi:10.1007/978-3-642-55334-9_8
fatcat:nkgzcka5kfgc5lrdnw6ptxbm3e
Good triangulations yield good tours
2008
Computers & Operations Research
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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. ...
doi:10.1016/j.cor.2006.03.025
fatcat:q7zovspt75clvjhq7wazcsoekq
Computational geometry and computer graphics
[chapter]
1993
Lecture Notes in Computer Science
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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. ...
doi:10.1007/bfb0029814
fatcat:auojepvbpvbf5km7qkti7vzxgy
Computational geometry and computer graphics
1992
Proceedings of the IEEE
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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. ...
doi:10.1109/5.163408
fatcat:qeintu3go5c35hxcvuifa7dgqm
Data-Gathering Scheme Using AUVs in Large-Scale Underwater Sensor Networks: A Multihop Approach
2016
Sensors
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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. ...
doi:10.3390/s16101626
pmid:27706042
pmcid:PMC5087414
fatcat:lne3z6oa4ncjrc7rxt6237oud4
Multi-robot coordination through dynamic Voronoi partitioning for informative adaptive sampling in communication-constrained environments
2017
2017 IEEE International Conference on Robotics and Automation (ICRA)
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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'. ...
doi:10.1109/icra.2017.7989245
dblp:conf/icra/KemnaRNYS17
fatcat:2g6v7ey47zbexlot2s7zzpkeqe
Near optimal minimal convex hulls of disks
2021
Journal of Global Optimization
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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 . ...
doi:10.1007/s10898-021-01002-5
fatcat:nyzgq3gwxbhc5jbhzconxxscy4
Distributed Multi-Actuator Control for Workload Balancing in Wireless Sensor and Actuator Networks
2011
IEEE Transactions on Automatic Control
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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 ...
doi:10.1109/tac.2011.2164035
fatcat:givgjrkzybf4jfu5smytlbpht4
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