Voronoi diagramsa survey of a fundamental geometric data structure

[1]  Kenneth L. Clarkson,et al.  Algorithms for diametral pairs and convex hulls that are optimal, randomized, and incremental , 1988, SCG '88.

[2]  Glenn K. Manacher,et al.  Neither the Greedy Nor the Delaunay Triangulation of a Planar Point Set Approximates the Optimal Triangulation , 1979, Inf. Process. Lett..

[3]  Christian Lantuéjoul,et al.  Geodesic methods in quantitative image analysis , 1984, Pattern Recognit..

[4]  A. L. Loeb.  A systematic survey of cubic crystal structures , 1970 .

[5]  Leonidas J. Guibas,et al.  Optimal Point Location in a Monotone Subdivision , 1986, SIAM J. Comput..

[6]  Ian K. Crain,et al.  The Monte-Carlo generation of random polygons , 1978 .

[7]  J. Linhart.  Die Beleuchtung Von Kugeln , 1981 .

[8]  David P. Dobkin,et al.  Delaunay graphs are almost as good as complete graphs , 1990, Discret. Comput. Geom..

[9]  A. Tversky,et al.  Nearest neighbors and Voronoi regions in certain point processes , 1983, Advances in Applied Probability.

[10]  Franz Aurenhammer,et al.  A new duality result concerning voronoi diagrams , 1986, ICALP.

[11]  Frank Dehne,et al.  A computational geometry approach to clustering problems , 1985, SCG '85.

[12]  Franz Aurenhammer,et al.  Power Diagrams: Properties, Algorithms and Applications , 1987, SIAM J. Comput..

[13]  Peter Forbes Rowat,et al.  Representing spatial experience and solving spatial problems in a simulated robot environment , 1979 .

[14]  Michael Ian Shamos,et al.  Geometric complexity , 1975, STOC.

[15]  Ethan D. Bolker,et al.  Recognizing Dirichlet tessellations , 1985 .

[16]  I. G. Gowda,et al.  Dynamic Voronoi diagrams , 1983, IEEE Trans. Inf. Theory.

[17]  WERNER NOWACKI.  Über allgemeine Eigenschaften von Wirkungsbereichen , 1976 .

[18]  Takao Asano,et al.  Voronoi Diagram for Points in a Simple Polygon , 1987 .

[19]  Bernard Chazelle,et al.  An Improved Algorithm for Constructing k th-Order Voronoi Diagrams , 1987, IEEE Trans. Computers.

[20]  Micha Sharir,et al.  A new efficient motion-planning algorithm for a rod in polygonal space , 1986, SCG '86.

[21]  Sabine Stifter,et al.  An Axiomatic Approach to Voronoi-Diagrams in 3D , 1991, J. Comput. Syst. Sci..

[22]  J. Kruskal.  On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[23]  Franz Aurenhammer,et al.  Recognising Polytopical Cell Complexes and Constructing Projection Polyhedra , 1987, J. Symb. Comput..

[24]  R. Seidel.  A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions , 1981 .

[25]  David G. Kirkpatrick,et al.  Optimal Search in Planar Subdivisions , 1983, SIAM J. Comput..

[26]  B. Boots.  Weighting Thiessen Polygons , 1980 .

[27]  Bernard Chazelle,et al.  Computing the Largest Empty Rectangle , 1986, SIAM J. Comput..

[28]  Franz Aurenhammer.  A relationship between Gale transforms and Voronoi diagrams , 1990, Discret. Appl. Math..

[29]  Mark H. Overmars,et al.  Dynamization of Order Decomposable Set Problems , 1981, J. Algorithms.

[30]  Anita Liu Chow.  Parallel algorithms for geometric problems , 1980 .

[31]  Robert L. Scot Drysdale,et al.  Voronoi diagrams based on convex distance functions , 1985, SCG '85.

[32]  D. Mount.  Voronoi Diagrams on the Surface of a Polyhedron. , 1985 .

[33]  Hans-Christoph Im Hof,et al.  Dirichlet regions in manifolds without conjugate points , 1979 .

[34]  G. L. Dirichlet.  Über die Reduction der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen. , 1850 .

[35]  David Eppstein,et al.  Finding the k Smallest Spanning Trees , 1990, BIT.

[36]  A. Brøndsted.  An Introduction to Convex Polytopes , 1982 .

[37]  Michael B. Dillencourt,et al.  A Non-Hamiltonian, Nondegenerate Delaunay Triangulation , 1987, Inf. Process. Lett..

[38]  Fionn Murtagh,et al.  A Survey of Recent Advances in Hierarchical Clustering Algorithms , 1983, Comput. J..

[39]  Micha Sharir,et al.  On the shortest paths between two convex polyhedra , 2018, JACM.

[40]  David G. Kirkpatrick,et al.  A Note on Delaunay and Optimal Triangulations , 1980, Inf. Process. Lett..

[41]  Nimrod Megiddo,et al.  Linear-time algorithms for linear programming in R3 and related problems , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[42]  D. T. Lee,et al.  Generalization of Voronoi Diagrams in the Plane , 1981, SIAM J. Comput..

[43]  R. Sokal,et al.  A New Statistical Approach to Geographic Variation Analysis , 1969 .

[44]  H. Blum.  Biological shape and visual science (part I) , 1973 .

[45]  W. Brostow,et al.  Coordination number in liquid argon , 1975 .

[46]  Robert E. Tarjan,et al.  Finding Minimum Spanning Trees , 1976, SIAM J. Comput..

[47]  Carl W David,et al.  Voronoi polyhedra as a tool for studying solvation structure , 1982 .

[48]  Hiroshi Imai,et al.  Minimax geometric fitting of two corresponding sets of points , 1989, SCG '89.

[49]  R Gambini.  A COMPUTER PROGRAM FOR CALCULATING LINES OF EQUILIBRIUM BETWEEN MULTIPLE CENTERS OF ATTRACTION , 1968 .

[50]  Kenneth L. Clarkson.  Further applications of random sampling to computational geometry , 1986, STOC '86.

[51]  W. Whiteley.  Realizability of Polyhedra , 1979 .

[52]  Raimund Seidel,et al.  Voronoi diagrams and arrangements , 1986, Discret. Comput. Geom..

[53]  Alok Aggarwal,et al.  Finding k Points with Minimum Diameter and Related Problems , 1991, J. Algorithms.

[54]  D. T. Lee,et al.  Generalized delaunay triangulation for planar graphs , 1986, Discret. Comput. Geom..

[55]  Ronald L. Graham,et al.  Some NP-complete geometric problems , 1976, STOC '76.

[56]  Raimund Seidel,et al.  Constructing higher-dimensional convex hulls at logarithmic cost per face , 1986, STOC '86.

[57]  Robin Sibson,et al.  Computing Dirichlet Tessellations in the Plane , 1978, Comput. J..

[58]  Samuel Rippa,et al.  Minimal roughness property of the Delaunay triangulation , 1990, Comput. Aided Geom. Des..

[59]  Michael Ian Shamos,et al.  Closest-point problems , 1975, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975).

[60]  B. Boots,et al.  Voronoi (Thiessen) polygons , 1987 .

[61]  L. Paul Chew,et al.  Guaranteed-Quality Triangular Meshes , 1989 .

[62]  D. F. Watson.  Computing the n-Dimensional Delaunay Tesselation with Application to Voronoi Polytopes , 1981, Comput. J..

[63]  F. Aurenhammer,et al.  On the Peeper's Voronoi diagram , 1991, SIGA.

[64]  Richard Cole,et al.  Merging Free Trees in Parallel for Efficient Voronoi Diagram Construction (Preliminary Version) , 1990, ICALP.

[65]  Andrew Chi-Chih Yao,et al.  On Constructing Minimum Spanning Trees in k-Dimensional Spaces and Related Problems , 1977, SIAM J. Comput..

[66]  Vitit KANTABUTRA,et al.  Traveling Salesman Cycles are not Always Subgraphs of Voronoi Duals , 1983, Inf. Process. Lett..

[67]  Richard J. Lipton,et al.  Multidimensional Searching Problems , 1976, SIAM J. Comput..

[68]  Ludwig August Seeber.  Recension der "Untersuchungen über die Eigenschaften der positiven ternären quadratischen Formen von Ludwig August Seeber". , 1840 .

[69]  Cyril Stanley Smith,et al.  The Shape of Things , 2019 .

[70]  Kevin Q. Brown,et al.  Voronoi Diagrams from Convex Hulls , 1979, Inf. Process. Lett..

[71]  Bruce W. Weide,et al.  Optimal Expected-Time Algorithms for Closest Point Problems , 1980, TOMS.

[72]  Branko Grünbaum,et al.  Tilings with congruent tiles , 1980 .

[73]  D. Matula,et al.  Properties of Gabriel Graphs Relevant to Geographic Variation Research and the Clustering of Points in the Plane , 2010 .

[74]  Carl Gutwin,et al.  The Delauney Triangulation Closely Approximates the Complete Euclidean Graph , 1989, WADS.

[75]  Franz Aurenhammer,et al.  A simple on-line randomized incremental algorithm for computing higher order Voronoi diagrams , 1992, Int. J. Comput. Geom. Appl..

[76]  D. T. Lee,et al.  On k-Nearest Neighbor Voronoi Diagrams in the Plane , 1982, IEEE Transactions on Computers.

[77]  Paul Chew,et al.  There is a planar graph almost as good as the complete graph , 1986, SCG '86.

[78]  Franz Aurenhammer,et al.  An optimal algorithm for constructing the weighted voronoi diagram in the plane , 1984, Pattern Recognit..

[79]  Charles S. Peskin,et al.  On the construction of the Voronoi mesh on a sphere , 1985 .

[80]  A. H. Thiessen.  PRECIPITATION AVERAGES FOR LARGE AREAS , 1911 .

[81]  Douglas J. Muder,et al.  Putting the best face on a Voronoi polyhedron , 1988 .

[82]  Raimund Seidel,et al.  On the number of faces in higher-dimensional Voronoi diagrams , 1987, SCG '87.

[83]  Narendra Ahuja,et al.  DOT PATTERN PROCESSING USING VORONOI POLYGONS AS NEIGHBORHOODS. , 1980 .

[84]  R. Seidel.  A Method for Proving Lower Bounds for Certain Geometric Problems , 1984 .

[85]  Herbert Edelsbrunner,et al.  An acyclicity theorem for cell complexes in d dimensions , 1989, SCG '89.

[86]  Robert Williams.  Space-Filling Polyhedron: Its Relation to Aggregates of Soap Bubbles, Plant Cells, and Metal Crystallites , 1968, Science.

[87]  ELKE KOCH,et al.  Wirkungsbereichspolyeder und Wirkungsbereichsteilungen zu kubischen Gitterkomplexen mit weniger als drei Freiheitsgraden , 1973 .

[88]  E. Gilbert.  Random Subdivisions of Space into Crystals , 1962 .

[89]  Rex A. Dwyer.  Higher-dimensional voronoi diagrams in linear expected time , 1991, Discret. Comput. Geom..

[90]  Bernard Chazelle,et al.  How to Search in History , 1983, Inf. Control..

[91]  Klaus H. Hinrichs,et al.  Plane-Sweep Solves the Closest Pair Problem Elegantly , 1988, Inf. Process. Lett..

[92]  Otfried Cheong,et al.  Euclidean minimum spanning trees and bichromatic closest pairs , 1991, Discret. Comput. Geom..

[93]  Denis Mollison,et al.  Spatial Contact Models for Ecological and Epidemic Spread , 1977 .

[94]  Robin Sibson,et al.  Locally Equiangular Triangulations , 1978, Comput. J..

[95]  Micha Sharir,et al.  Intersection and Closest-Pair Problems for a Set of Planar Discs , 1985, SIAM J. Comput..

[96]  J. Goodisman,et al.  Voronoi cells: An interesting and potentially useful cell model for interpreting the small‐angle scattering of catalysts , 1983 .

[97]  Derick Wood,et al.  Voronoi Diagrams Based on General Metrics in the Plane , 1988, STACS.

[98]  Chak-Kuen Wong,et al.  On Some Distance Problems in Fixed Orientations , 1987, SIAM J. Comput..

[99]  Tetsuo Asano,et al.  Clustering algorithms based on minimum and maximum spanning trees , 1988, SCG '88.

[100]  D. H. McLain,et al.  Two Dimensional Interpolation from Random Data , 1976, Comput. J..

[101]  Kevin Q. Brown.  Geometric transforms for fast geometric algorithms , 1979 .

[102]  F. P. Preparata,et al.  Convex hulls of finite sets of points in two and three dimensions , 1977, CACM.

[103]  Hans Rohnert.  Moving Discs Between Polygons , 1988, ICALP.

[104]  F. Aurenhammer.  Linear combinations from power domains , 1988 .

[105]  J. Besag.  Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[106]  David M. Mount.  Storing the subdivision of a polyhedral surface , 1987, Discret. Comput. Geom..

[107]  Pravin M. Vaidya,et al.  Geometry helps in matching , 1989, STOC '88.

[108]  Alok Aggarwal,et al.  Solving query-retrieval problems by compacting Voronoi diagrams , 1990, STOC '90.

[109]  Steven Fortune.  A Fast Algorithm for Polygon Containment by Translation (Extended Abstract) , 1985, ICALP.

[110]  Takao Asano,et al.  A new point-location algorithm and its practical efficiency: comparison with existing algorithms , 1984, TOGS.

[111]  Franz Aurenhammer,et al.  Improved Algorithms for Discs and Balls Using Power Diagrams , 1988, J. Algorithms.

[112]  Hiroshi Imai,et al.  Voronoi Diagram in the Laguerre Geometry and its Applications , 1985, SIAM J. Comput..

[113]  Douglas J. Muder.  How Big is an n-Sided Voronoi Polygon? , 1990 .

[114]  John A. Hartigan,et al.  Clustering Algorithms , 1975 .

[115]  D. T. Lee,et al.  Two-Dimensional Voronoi Diagrams in the Lp-Metric , 1980, J. ACM.

[116]  F. Aurenhammer,et al.  Geometric relations among Voronoi diagrams , 1987, STACS.

[117]  Bruce Randall Donald,et al.  Simplified Voronoi diagrams , 1987, SCG '87.

[118]  Kurt Mehlhorn,et al.  On the construction of abstract voronoi diagrams , 1990, STACS.

[119]  David B. Arnold,et al.  The Use of Voronoi Tessellations in Processing Soil Survey Results , 1984, IEEE Computer Graphics and Applications.

[120]  Leonidas J. Guibas,et al.  Parallel computational geometry , 1988, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[121]  Kenneth J. Supowit,et al.  The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees , 1983, JACM.

[122]  A. Lingus,et al.  The Greedy and Delaunay Triangulations are Not Bad in the Average Case , 1986, Inf. Process. Lett..

[123]  David M. Mount,et al.  Globally-Equiangular triangulations of co-circular points in 0(n log n) time , 1988, SCG '88.

[124]  J. L Finney,et al.  A procedure for the construction of Voronoi polyhedra , 1979 .

[125]  Joseph S. B. Mitchell,et al.  The Discrete Geodesic Problem , 1987, SIAM J. Comput..

[126]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[127]  E. Bolker,et al.  Generalized Dirichlet tessellations , 1986 .

[128]  D. A. Field,et al.  Implementing Watson's algorithm in three dimensions , 1986, SCG '86.

[129]  Richard J. Kopec.  AN ALTERNATIVE METHOD FOR THE CONSTRUCTION OF THIESSEN POLYGONS , 1963 .

[130]  W. A. Johnson.  Reaction Kinetics in Processes of Nucleation and Growth , 1939 .

[131]  T. Kiang.  RANDOM FRAGMENTATION IN TWO AND THREE DIMENSIONS. , 1966 .

[132]  Christos H. Papadimitriou,et al.  The Euclidean Traveling Salesman Problem is NP-Complete , 1977, Theor. Comput. Sci..

[133]  Chee-Keng Yap,et al.  A "Retraction" Method for Planning the Motion of a Disc , 1985, J. Algorithms.

[134]  Bernard Chazelle,et al.  Halfspace range search: An algorithmic application ofk-sets , 1986, Discret. Comput. Geom..

[135]  Adrian Bowyer,et al.  Computing Dirichlet Tessellations , 1981, Comput. J..

[136]  D. Weaire,et al.  Soap, cells and statistics – random patterns in two dimensions , 1984 .

[137]  Michael B. Dillencourt.  Toughness and Delaunay triangulations , 1990, Discret. Comput. Geom..

[138]  Hartmut Noltemeier,et al.  On Separable Clusterings , 1989, J. Algorithms.

[139]  Daniel J. Rosenkrantz,et al.  An analysis of several heuristics for the traveling salesman problem , 2013, Fundamental Problems in Computing.

[140]  Steven Fortune,et al.  A sweepline algorithm for Voronoi diagrams , 1986, SCG '86.

[141]  Richard Cole,et al.  New Upper Bounds for Neighbor Searching , 1986, Inf. Control..

[142]  Leonidas J. Guibas,et al.  Points and triangles in the plane and halving planes in space , 1991, Discret. Comput. Geom..

[143]  Klara Kedem,et al.  Placing the largest similar copy of a convex polygon among polygonal obstacles , 1989, SCG '89.

[144]  V. Klee.  On the complexity ofd- dimensional Voronoi diagrams , 1979 .

[145]  N. J. A. Sloane,et al.  Voronoi regions of lattices, second moments of polytopes, and quantization , 1982, IEEE Trans. Inf. Theory.

[146]  Leonidas J. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[147]  Ugo Montanari,et al.  A Method for Obtaining Skeletons Using a Quasi-Euclidean Distance , 1968, J. ACM.

[148]  Robert L. Scot Drysdale,et al.  A practical algorithm for computing the Delaunay triangulation for convex distance functions , 1990, SODA '90.

[149]  John Fairfield,et al.  Segmenting Dot Patterns by Voronoi Diagram Concavity , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.