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Round-Tour Voronoi Diagrams

2009
*
2009 Sixth International Symposium on Voronoi Diagrams
*

We call this partitioning a "

doi:10.1109/isvd.2009.9
dblp:conf/isvd/FujiiS09
fatcat:koxcwh5mmrhkxjzg7jtykn7dwy
*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. ...##
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Round-Trip Voronoi Diagrams and Doubling Density in Geographic Networks
[article]

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

arXiv:1005.1053v1
fatcat:7kgmdsg2b5biresnmp6ahvev5a
*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). ...##
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Intersections with random geometric objects

1998
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Computational geometry
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Using this result, we explore the intersection complexity of a random

doi:10.1016/s0925-7721(98)00004-2
fatcat:fpbk62ycsbbd7ahj6hebtsfscm
*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*...##
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Adaptive Deployment of Mobile Robotic Networks

2013
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IEEE Transactions on Automatic Control
*

In particular, if , then the generalized

doi:10.1109/tac.2012.2215512
fatcat:t77tlr3ztjgwhbb7cdpkalom64
*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. ...##
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Representation of Imprecise Digital Objects
[chapter]

2016
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Lecture Notes in Computer Science
*

The additivelymultplicatively distance is associated with the so-called compoundly-weighted

doi:10.1007/978-3-319-32360-2_31
fatcat:ksztnmwcsrfurk746ooyp2rsge
*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. ...##
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Fast Parallel Algorithms for Euclidean Minimum Spanning Tree and Hierarchical Spatial Clustering
[article]

2021
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arXiv
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pre-print

This ordinary

arXiv:2104.01126v1
fatcat:c3ocmhisqfcqrfpyudtfmqmhyi
*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] . ...##
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New Algorithms Based on the Voronoi Diagram Applied in a Pilot Study on Normal Mucosa and Carcinomas

2000
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Analytical Cellular Pathology
*

To assess a possible diagnostic and prognostic value of quantitiative tissue architecture analysis, structural features based on the

doi:10.1155/2000/389361
pmid:11310643
pmcid:PMC4618427
fatcat:avcagina2jayjp6mgsyponeq44
*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). ...##
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ForestMaps: A Computational Model and Visualization for Forest Utilization
[chapter]

2014
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Lecture Notes in Computer Science
*

Fig. 3 . 3 Left: a small artificial example of a street

doi:10.1007/978-3-642-55334-9_8
fatcat:nkgzcka5kfgc5lrdnw6ptxbm3e
*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. ...##
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Good triangulations yield good tours

2008
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Computers & Operations Research
*

Indeed, our experiments show that the resulting

doi:10.1016/j.cor.2006.03.025
fatcat:q7zovspt75clvjhq7wazcsoekq
*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. ...##
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Computational geometry and computer graphics
[chapter]

1993
*
Lecture Notes in Computer Science
*

The Delaunay triangulation and

doi:10.1007/bfb0029814
fatcat:auojepvbpvbf5km7qkti7vzxgy
*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. ...##
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Computational geometry and computer graphics

1992
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Proceedings of the IEEE
*

The Delaunay triangulation and

doi:10.1109/5.163408
fatcat:qeintu3go5c35hxcvuifa7dgqm
*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. ...##
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Data-Gathering Scheme Using AUVs in Large-Scale Underwater Sensor Networks: A Multihop Approach

2016
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Sensors
*

Figure 5 . 5 Acoustic Sensor Network with

doi:10.3390/s16101626
pmid:27706042
pmcid:PMC5087414
fatcat:lne3z6oa4ncjrc7rxt6237oud4
*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. ...##
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Multi-robot coordination through dynamic Voronoi partitioning for informative adaptive sampling in communication-constrained environments

2017
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2017 IEEE International Conference on Robotics and Automation (ICRA)
*

We use an approach that combines

doi:10.1109/icra.2017.7989245
dblp:conf/icra/KemnaRNYS17
fatcat:2g6v7ey47zbexlot2s7zzpkeqe
*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'. ...##
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Near optimal minimal convex hulls of disks

2021
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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

doi:10.1007/s10898-021-01002-5
fatcat:nyzgq3gwxbhc5jbhzconxxscy4
*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 . ...##
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Distributed Multi-Actuator Control for Workload Balancing in Wireless Sensor and Actuator Networks

2011
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IEEE Transactions on Automatic Control
*

We applied a simple partition method,

doi:10.1109/tac.2011.2164035
fatcat:givgjrkzybf4jfu5smytlbpht4
*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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