Relative neighborhood graphs and their relatives

Results of neighborhood graphs are surveyed. Properties, bounds on the size, algorithms, and variants of the neighborhood graphs are discussed. Numerous applications including computational morphology, spatial analysis, pattern classification, and databases for computer vision are described. >

[1]  Franjo Pernus.  The Delaunay triangulation and the shape hull as tools in muscle fibre analysis , 1988, Pattern Recognit. Lett..

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

[3]  Leonidas J. Guibas,et al.  Slimming down by adding; selecting heavily covered points , 1990, SCG '90.

[4]  Luc Devroye,et al.  On the Inequality of Cover and Hart in Nearest Neighbor Discrimination , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  D. W. Dearholt,et al.  Monotonic Search Networks For Computer Vision Databases , 1988, Twenty-Second Asilomar Conference on Signals, Systems and Computers.

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

[7]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[8]  William Dunham,et al.  Journey through Genius: The Great Theorems of Mathematics , 1990 .

[9]  John D. Radke,et al.  On the Shape of a Set of Points , 1988 .

[10]  Mark H. Overmars,et al.  New methods for computing visibility graphs , 1988, SCG '88.

[11]  P. Erdös,et al.  Geometrical Extrema Suggested by a Lemma of Besicovitch , 1951 .

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

[13]  Robert E. Tarjan,et al.  Data structures and network algorithms , 1983, CBMS-NSF regional conference series in applied mathematics.

[14]  L. Devroye.  THE EXPECTED SIZE OF SOME GRAPHS IN COMPUTATIONAL GEOMETRY , 1988 .

[15]  Ruei-Chuan Chang,et al.  Computing the k-relative neighborhood graphs in Euclidean plane , 1991, Pattern Recognit..

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

[17]  Nen-Fu Huang.  A divide-and-conquer algorithm for constructing relative neighborhood graph , 1990, BIT Comput. Sci. Sect..

[18]  D. T. Lee.  Relative neighborhood graphs in the Li-metric , 1985, Pattern Recognit..

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

[20]  Bernard Chazelle.  Filtering Search: A New Approach to Query-Answering , 1983, FOCS.

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

[22]  Charles T. Zahn,et al.  Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters , 1971, IEEE Transactions on Computers.

[23]  Kenneth L. Clarkson,et al.  Combinatorial complexity bounds for arrangements of curves and surfaces , 2015, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[24]  Leonidas J. Guibas,et al.  Combinatorial complexity bounds for arrangements of curves and spheres , 1990, Discret. Comput. Geom..

[25]  Jyrki Katajaien,et al.  The region approach for computing relative neighborhood graphs in the L p metric , 1988 .

[26]  Dan E. Willard,et al.  On the Angle Restricted Nearest Neighbor Problem , 1990, Inf. Process. Lett..

[27]  R. Urquhart.  Algorithms for computation of relative neighbourhood graph , 1980 .

[28]  Olli Nevalainen,et al.  Computing relative neighbourhood graphs in the plane , 1986, Pattern Recognit..

[29]  J M Kennedy,et al.  Illusory Contours Can Arise in Dot Figures , 1978, Perception.

[30]  Mark H. Overmars,et al.  Batched Dynamic Solutions to Decomposable Searching Problems , 1985, J. Algorithms.

[31]  Ralf Hartmut Güting,et al.  The direct dominance problem , 1985, SCG '85.

[32]  Micha Sharir,et al.  A Hyperplane Incidence Problem with Applications to Counting Distances , 1990, SIGAL International Symposium on Algorithms.

[33]  Roderick Urquhart,et al.  Some properties of the planar Euclidean relative neighbourhood graph , 1983, Pattern Recognit. Lett..

[34]  Manabu Ichino,et al.  The relative neighborhood graph for mixed feature variables , 1985, Pattern Recognit..

[35]  Bernard Chazelle,et al.  Quasi-optimal upper bounds for simplex range searching and new zone theorems , 1990, SCG '90.

[36]  Günter Rote,et al.  Testing the Necklace Condition for Shortest Tours and Optimal Factors in the Plane , 1987, ICALP.

[37]  E. R. Reifenberg.  A Problem on Circles , 1948 .

[38]  G. Klincsek.  Minimal Triangulations of Polygonal Domains , 1980 .

[39]  W. W. Moss.  Some New Analytic and Graphic Approaches to Numerical Taxonomy, with an Example from the Dermanyssidae (ACARI) , 1967 .

[40]  Godfried T. Toussaint,et al.  Computational Geometry and Morphology , 1986 .

[41]  Thomas Ottmann,et al.  Algorithms for Reporting and Counting Geometric Intersections , 1979, IEEE Transactions on Computers.

[42]  L. Lefkovitch,et al.  Further nonparametric tests for comparing dissimilarity matrices based on the relative neighborhood graph , 1985 .

[43]  Godfried T. Toussaint,et al.  The relative neighbourhood graph of a finite planar set , 1980, Pattern Recognit..

[44]  Jirí Matousek,et al.  Relative neighborhood graphs in three dimensions , 1992, SODA '92.

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

[46]  Jerzy W. Jaromczyk,et al.  A note on relative neighborhood graphs , 1987, SCG '87.

[47]  Remco C. Veltkamp,et al.  The gamma-neighborhood Graph , 1992, Comput. Geom..

[48]  D. Avis,et al.  REMARKS ON THE SPHERE OF INFLUENCE GRAPH , 1985 .

[49]  Pravin M. Vaidya,et al.  AnO(n logn) algorithm for the all-nearest-neighbors Problem , 1989, Discret. Comput. Geom..

[50]  Jukka Teuhola,et al.  A Linear Expected-Time Algorithm for Computing Planar Relative Neighbourhood Graphs , 1987, Inf. Process. Lett..

[51]  Leonidas J. Guibas,et al.  A linear-time algorithm for computing the voronoi diagram of a convex polygon , 1989, Discret. Comput. Geom..

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

[53]  R. Lawlor,et al.  Sacred Geometry: Philosophy and Practice , 1982 .

[54]  Robert E. Tarjan,et al.  Scaling and related techniques for geometry problems , 1984, STOC '84.

[55]  Jon Louis Bentley,et al.  An Algorithm for Finding Best Matches in Logarithmic Expected Time , 1977, TOMS.

[56]  Fan Chung.  Sphere-and-point incidence relations in high dimensions with applications to unit distances and furthest-neighbor pairs , 1989 .

[57]  David G. Kirkpatrick,et al.  On the shape of a set of points in the plane , 1983, IEEE Trans. Inf. Theory.

[58]  Robert E. Tarjan,et al.  A Linear-Time Algorithm for a Special Case of Disjoint Set Union , 1985, J. Comput. Syst. Sci..

[59]  Chuan Yi Tang,et al.  20-relative Neighborhood Graphs Are Hamiltonian , 1991, J. Graph Theory.

[60]  Joseph O'Rourke.  Computing the relative neighborhood graph in the L1 and Linfinity metrics , 1982, Pattern Recognit..

[61]  Jerzy W. Jaromczyk,et al.  Constructing the relative neighborhood graph in 3-dimensional Euclidean space , 1991, Discret. Appl. Math..

[62]  Godfried T. Toussaint.  Some Unsolved Problems on Proximity Graphs , 1991 .

[63]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

[64]  Arne Maus,et al.  Delaunay triangulation and the convex hull ofn points in expected linear time , 1984, BIT.

[65]  Stephan Olariu.  A Simple Linear-Time Algorithm for Computing the RNG and MST of Unimodal Polygons , 1989, Inf. Process. Lett..

[66]  D. Kirkpatrick,et al.  A Framework for Computational Morphology , 1985 .

[67]  R. E. Miles.  On the homogeneous planar Poisson point process , 1970 .

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

[69]  Rex A. Dwyer,et al.  Average-case analysis of algorithms for convex hulls and Voronoi diagrams , 1988 .

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

[71]  G. Matheron.  Random Sets and Integral Geometry , 1976 .

[72]  Olli Nevalainen,et al.  An Almost Naive Algorithm for Finding Relative Neighbourhood Graphs in Lp Metrics , 1987, RAIRO Theor. Informatics Appl..

[73]  Ruei-Chuan Chang,et al.  Computing the constrained relative neighborhood graphs and constrained gabriel graphs in Euclidean plane , 1991, Pattern Recognit..

[74]  D. J. Langridge,et al.  A Computational View of Perception , 1973, Perception.

[75]  D. T. Lee,et al.  Location of a point in a planar subdivision and its applications , 1976, STOC '76.

[76]  Dan E. Willard,et al.  New Data Structures for Orthogonal Range Queries , 1985, SIAM J. Comput..

[77]  Václav Medek.  On the boundary of a finite set of points in the plane , 1981 .

[78]  Chuan Yi Tang,et al.  Solving the Euclidean Bottleneck Biconnected Edge Subgraph Problem by 2-Relative Neighborhood Graphs , 1992, Discret. Appl. Math..

[79]  G. Rothe.  Two solvable cases of the Traveling Salesman Problem , 1988 .

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

[81]  Godfried T. Toussaint,et al.  Computing the Relative Neighbour Decomposition of a Simple Polygon , 1988 .

[82]  S. Yokoi,et al.  Voronoi and Related Neighbors on Digitized two-Dimensional Space with Applications to Texture Analysis , 1988 .

[83]  Leonidas J. Guibas,et al.  On Computing All North-East Nearest Neighbors in the L1 Metric , 1983, Inf. Process. Lett..

[84]  Ruei-Chuan Chang,et al.  The K-Gabriel Graphs and Their Applications , 1990, SIGAL International Symposium on Algorithms.

[85]  Warren D. Smith.  Studies in computational geometry motivated by mesh generation , 1989 .

[86]  Arthur Getis,et al.  Models of spatial processes : an approach to the study of point, line, and area patterns , 1979 .

[87]  Tiow Seng Tan,et al.  A quadratic time algorithm for the minmax length triangulation , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[88]  G. Toussaint.  A Graph-Theoretical Primal Sketch , 1988 .

[89]  L. P. Lefkovitch,et al.  Species Associations and Conditional Clustering: Clustering With or Without Pairwise Resemblances , 1987 .

[90]  L. Lefkovitch,et al.  A Nonparametric Method for Comparing Dissimilarity Matrices, a General Measure of Biogeographical Distance, and Their Application , 1984, The American Naturalist.

[91]  Franz Aurenhammer,et al.  Voronoi diagrams—a survey of a fundamental geometric data structure , 1991, CSUR.

[92]  Herbert Edelsbrunner,et al.  Three-dimensional alpha shapes , 1992, VVS.

[93]  Peter E. Hart,et al.  Nearest neighbor pattern classification , 1967, IEEE Trans. Inf. Theory.