@article{4112, abstract = {The batched static version of a searching problem asks for performing a given set of queries on a given set of objects. All queries are known in advance. The batched dynamic version of a searching problem is the following: given a sequence of insertions, deletions, and queries, perform them on an initially empty set. We will develop methods for solving batched static and batched dynamic versions of searching problems which are in particular applicable to decomposable searching problems. The techniques show that batched static (dynamic) versions of searching problems can often be solved more efficiently than by using known static (dynamic) data structures. In particular, a technique called “streaming” is described that reduces the space requirements considerably. The methods have also a number of applications on set problems. E.g., the k intersecting pairs in a set of n axis-parallel hyper-rectangles in d dimensions can be reported in O (nlogd−1n + k) time using only O(n) space.}, author = {Edelsbrunner, Herbert and Overmars, Mark}, issn = {1090-2678}, journal = {Journal of Algorithms}, number = {4}, pages = {515 -- 542}, publisher = {Elsevier}, title = {{Batched dynamic solutions to decomposable searching problems}}, doi = {10.1016/0196-6774(85)90030-6}, volume = {6}, year = {1985}, } @article{4113, abstract = {Let S denote a set of n points in the Euclidean plane. A subset S′ of S is termed a k-set of S if it contains k points and there exists a straight line which has no point of S on it and separates S′ from S−S′. We let fk(n) denote the maximum number of k-sets which can be realized by a set of n points. This paper studies the asymptotic behaviour of fk(n) as this function has applications to a number of problems in computational geometry. A lower and an upper bound on fk(n) is established. Both are nontrivial and improve bounds known before. In particular, is shown by exhibiting special point-sets which realize that many k-sets. In addition, is proved by the study of a combinatorial problem which is of interest in its own right.}, author = {Edelsbrunner, Herbert and Welzl, Emo}, issn = {1096-0899}, journal = {Journal of Combinatorial Theory Series A}, number = {1}, pages = {15 -- 29}, publisher = {Elsevier}, title = {{On the number of line separations of a finite set in the plane}}, doi = {10.1016/0097-3165(85)90017-2}, volume = {38}, year = {1985}, } @article{4114, abstract = {Proportional link linkage (PLL) clustering methods are a parametric family of monotone invariant agglomerative hierarchical clustering methods. This family includes the single, minimedian, and complete linkage clustering methods as special cases; its members are used in psychological and ecological applications. Since the literature on clustering space distortion is oriented to quantitative input data, we adapt its basic concepts to input data with only ordinal significance and analyze the space distortion properties of PLL methods. To enable PLL methods to be used when the numbern of objects being clustered is large, we describe an efficient PLL algorithm that operates inO(n 2 logn) time andO(n 2) space}, author = {Day, William and Edelsbrunner, Herbert}, issn = {1432-1343}, journal = {Journal of Classification}, number = {2-3}, pages = {239 -- 254}, publisher = {Springer}, title = {{Investigation of Proportional Link Linkage Clustering Methods}}, doi = {10.1007/BF01908077}, volume = {2}, year = {1985}, } @article{4115, abstract = {A polygon in the plane is convex if it contains all line segments connecting any two of its points. Let P and Q denote two convex polygons. The computational complexity of finding the minimum and maximum distance possible between two points p in P and q in Q is studied. An algorithm is described that determines the minimum distance (together with points p and q that realize it) in O(logm + logn) time, where m and n denote the number of vertices of P and Q, respectively. This is optimal in the worst case. For computing the maximum distance, a lower bound Ω(m + n) is proved. This bound is also shown to be best possible by establishing an upper bound of O(m + n).}, author = {Edelsbrunner, Herbert}, issn = {1090-2678}, journal = {Journal of Algorithms}, number = {2}, pages = {213 -- 224}, publisher = {Academic Press}, title = {{Computing the extreme distances between two convex polygons}}, doi = {10.1016/0196-6774(85)90039-2}, volume = {6}, year = {1985}, } @article{4116, abstract = {A straight line that intersects all members of a set S of objects in the real plane is called a transversal of S. Geometric transforms are described that reduce transversal problems for various types of objects to convex hull problems for points. These reductions lead to efficient algorithms for finding transversals which are also described. Applications of the algorithms are found in computer graphics: “Reproduce the line displayed by a collection of pixels”, and in statistics: “Find the line that minimizes the maximum distance from a collection of (weighted) points in the plane”.}, author = {Edelsbrunner, Herbert}, issn = {0304-3975}, journal = {Theoretical Computer Science}, number = {1}, pages = {55 -- 69}, publisher = {Elsevier}, title = {{Finding Transversals for Sets of Simple Geometric-Figures}}, doi = {10.1016/0304-3975(85)90005-2}, volume = {35}, year = {1985}, } @article{4120, abstract = {Let P be a set of n points in the Euclidean plane and let C be a convex figure. We study the problem of preprocessing P so that for any query point q, the points of P in C+q can be retrieved efficiently. If constant time sumces for deciding the inclusion of a point in C, we then demonstrate the existence of an optimal solution: the algorithm requires O(n) space and O(k + log n) time for a query with output size k. If C is a disk, the problem becomes the wellknown fixed-radius neighbour problem, to which we thus provide the first known optimal solution.}, author = {Chazelle, Bernard and Edelsbrunner, Herbert}, issn = {1095-855X}, journal = {Journal of Symbolic Computation}, number = {1}, pages = {47 -- 56}, publisher = {Elsevier}, title = {{Optimal solutions for a class of point retrieval problems}}, doi = {10.1016/S0747-7171(85)80028-6}, volume = {1}, year = {1985}, } @inbook{4241, author = {Curtis, C. and Curtis, J. and Barton, Nicholas H}, booktitle = {Genetic Control of Host Resistance to Infection and Malignancy}, editor = {Skamene, Emil}, isbn = {9780845141021}, publisher = {Liss}, title = {{Methodology for testing the hypothesis of single locus control of host resistance to infection and malignancy}}, volume = {3}, year = {1985}, } @article{4325, author = {Jones, Steve and Barton, Nicholas H}, journal = {Nature}, pages = {668 -- 668}, publisher = {Nature Publishing Group}, title = {{Haldane's Rule OK}}, doi = {10.1038/314668a0}, volume = {314}, year = {1985}, } @article{4326, author = {Barton, Nicholas H and Hewitt, Godfrey}, issn = {1545-2069}, journal = {Annual Review of Ecology and Systematics}, pages = {113 -- 148}, publisher = {Annual Reviews}, title = {{Analysis of hybrid zones}}, doi = {10.1146/annurev.es.16.110185.000553}, volume = {16}, year = {1985}, } @inproceedings{3513, author = {Dobkin, David and Edelsbrunner, Herbert}, booktitle = {9th International Workshop on Graph Theoretic Concepts in Computer Science}, isbn = {3-853-20311-6}, location = {Haus Ohrbeck, Germany}, pages = {88 -- 99}, publisher = {Teubner}, title = {{Ham-sandwich theorems applied to intersection problems}}, year = {1984}, } @article{4117, abstract = {Two or more geometrical objects (solids) are said to be connected whenever their union is a connected point set in the usual sense. Sets of geometrical objects are naturally divided into connected components, which are maximal connected subsets. We show that the connected components of a given collection of n horizontal and vertical line segments in the plane can be computed in O (n log n) time and O (n) space and prove that this is essentially optimal. The result is generalized to compute the connected components of a set of n rectilinearly-oriented rectangles in the plane with the same time and space bounds. Several extensions of the results to higher dimensions and to dynamic sets of objects are discussed.}, author = {Edelsbrunner, Herbert and Van Leeuwen, Jan and Ottmann, Thomas and Wood, Derick}, issn = {1290-385X}, journal = {Rairo-Informatique Theorique Et Applications-Theoretical Informatics and Applications}, number = {2}, pages = {171 -- 183}, publisher = {EDP Sciences}, title = {{Computing the connected components of simple rectilinear geometrical objects in D-Space}}, doi = {10.1051/ita/1984180201711}, volume = {18}, year = {1984}, } @article{4118, abstract = {A rectilinear polygon can be viewed as an art gallery room whose walls meet at right angles. An algorithm is presented that stations guards in such a room so that every interior point is visible to some guard. The algorithm partitions the polygon into L-shaped pieces, a subclass of star-shaped pieces, and locates one guard within each kernel. The algorithm runs in O(n log n) time in the worst case for a polygon of n vertices.}, author = {Edelsbrunner, Herbert and O'Rourke, Joseph and Welzl, Emo}, issn = {0734-189X}, journal = {Computer Vision, Graphics, and Image Processing}, number = {2}, pages = {167 -- 176}, publisher = {Elsevier}, title = {{Stationing guards in rectilinear art galleries}}, doi = {10.1016/S0734-189X(84)80041-9}, volume = {27}, year = {1984}, } @inproceedings{4119, author = {Edelsbrunner, Herbert and Welzl, Emo}, booktitle = {11th International Symposium on Mathematical Foundations of Computer Science}, isbn = {3-540-13372-0}, location = {Praha, Czechoslovakia}, pages = {265 -- 272}, publisher = {Springer}, title = {{Monotone edge sequences in line arrangements and applications}}, doi = {10.1007/BFb0030307}, volume = {176}, year = {1984}, } @article{4121, abstract = {Whenevern objects are characterized by a matrix of pairwise dissimilarities, they may be clustered by any of a number of sequential, agglomerative, hierarchical, nonoverlapping (SAHN) clustering methods. These SAHN clustering methods are defined by a paradigmatic algorithm that usually requires 0(n 3) time, in the worst case, to cluster the objects. An improved algorithm (Anderberg 1973), while still requiring 0(n 3) worst-case time, can reasonably be expected to exhibit 0(n 2) expected behavior. By contrast, we describe a SAHN clustering algorithm that requires 0(n 2 logn) time in the worst case. When SAHN clustering methods exhibit reasonable space distortion properties, further improvements are possible. We adapt a SAHN clustering algorithm, based on the efficient construction of nearest neighbor chains, to obtain a reasonably general SAHN clustering algorithm that requires in the worst case 0(n 2) time and space. Whenevern objects are characterized byk-tuples of real numbers, they may be clustered by any of a family of centroid SAHN clustering methods. These methods are based on a geometric model in which clusters are represented by points ink-dimensional real space and points being agglomerated are replaced by a single (centroid) point. For this model, we have solved a class of special packing problems involving point-symmetric convex objects and have exploited it to design an efficient centroid clustering algorithm. Specifically, we describe a centroid SAHN clustering algorithm that requires 0(n 2) time, in the worst case, for fixedk and for a family of dissimilarity measures including the Manhattan, Euclidean, Chebychev and all other Minkowski metrics.}, author = {Day, William and Edelsbrunner, Herbert}, issn = {1432-1343}, journal = {Journal of Classification}, pages = {7 -- 24}, publisher = {Springer}, title = {{Efficient algorithms for agglomerative hierarchical clustering methods}}, doi = {10.1007/BF01890115}, volume = {1}, year = {1984}, } @inproceedings{4122, abstract = {Computational geometry, considered a subfield of computer science, is concerned with the computational aspects of geometric problems. The increasing activity in this rather young field made it split into several reasonably independent subareas. This paper presents several key-problems of the classical part of computational geometry which exhibit strong interrelations. A unified view of the problems is stressed, and the general ideas behind the methods that solve them are worked out.}, author = {Edelsbrunner, Herbert}, booktitle = {1st Symposium of Theoretical Aspects of Computer Science}, isbn = {3-540-12920-0}, location = {Paris, France}, pages = {1 -- 13}, publisher = {Springer}, title = {{Key-problems and key-methods in computational geometry}}, doi = {10.1007/3-540-12920-0_1}, volume = {166}, year = {1984}, } @article{4123, abstract = {Windowing a two-dimensional picture means to determine those line segments of the picture that are visible through an axis-parallel window. A study of some algorithmic problems involved in windowing a picture is offered. Some methods from computational geometry are exploited to store the picture in a computer such that (1) those line segments inside or partially inside of a window can be determined efficiently, and (2) the set of those line segments can be maintained efficiently while the window is moved parallel to a coordinate axis and/or it is enlarged or reduced.}, author = {Edelsbrunner, Herbert and Overmars, Mark and Seidel, Raimund}, issn = {1557-895X}, journal = {Computer Vision, Graphics, and Image Processing}, number = {1}, pages = {92 -- 108}, publisher = {Elsevier}, title = {{Some methods of computational geometry applied to computer graphics}}, doi = {10.1016/0734-189X(84)90142-7}, volume = {28}, year = {1984}, } @article{4327, author = {Barton, Nicholas H and Charlesworth, Brian}, issn = {1545-2069}, journal = {Annual Review of Ecology and Systematics}, pages = {133 -- 164}, publisher = {Annual Reviews}, title = {{Genetic revolutions, founder effects, and speciation}}, doi = {10.1146/annurev.es.15.110184.001025}, volume = {15}, year = {1984}, } @inbook{3562, abstract = {The segment tree is a data structure for storing and maintaining a set of intervals on the real line. It has been used for an efficient algorithmic approach in a variety of geometric problems including the problem of deter-mining intersections among axis-parallel rectangles, computing the measure of a set of axis-parallel rectangles, and locating a point in a planar subdivision. A segment tree for n intervals requires 0(n) space in the best case and 0(n log n) space in the worst case. It is shown that segment trees require 0(n log n) space even in the expected case. Additionally, the worst-case upper bound on the space requirement of segment trees is improved over the previously known bound. Surprisingly, the space requirements in the expected and in the worst case differ only little. }, author = {Bucher, W. and Edelsbrunner, Herbert}, booktitle = {Computational Geometry: Theory and Applications}, editor = {Preparata, Franco}, pages = {109 -- 125}, publisher = {Elsevier}, title = {{On expected- and worst-case segment trees}}, volume = {1}, year = {1983}, } @inbook{3563, abstract = {Usually in computer graphics, a two-dimensional view of a set of three-dimensional objects is considered. In this article we reduce the dimensionality by one in each case. In other words we study what, for obvious reasons, we call Flatland graphics. This forms the beginning of a mathematical investigation of computer graphics and, at the same time, provides uniform solutions for a number of computational geometry problems. In particular we study the maintenance of a view during insertion and deletion of objects and the "frame-to-frame" coherence while walking around a set of objects. Both parallel and perspective projections are considered. Our major concern is convex objects that are simple—in a sense, made precise in this article. However, we will close this article by discussing some possible extensions to nonconvex objects and/or to higher dimensions. The investigation also serves to demonstrate a number of tools that have been developed recently in the context of computational geometry. For example. dynamization and searching. }, author = {Edelsbrunner, Herbert and Overmars, Mark and Wood, Derick}, booktitle = {Computational Geometry: Theory and Applications}, editor = {Preparata, Franco}, isbn = {0-89232-356-6}, pages = {35 -- 59}, publisher = {Elsevier}, title = {{Graphics in Flatland: a case study}}, volume = {1}, year = {1983}, } @inbook{3564, author = {Edelsbrunner, Herbert}, booktitle = {Überblicke Informationsverarbeitung }, editor = {Maurer, Hermann}, isbn = {9783411016587}, pages = {55 -- 109}, publisher = {BI Wissenschaftsverlag}, title = {{Neue Entwicklungen im Bereich Datenstrukturen}}, year = {1983}, }