@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}, } @article{3598, author = {Barton, Nicholas H and Jones, Steve}, issn = {1476-4687}, journal = {Nature}, pages = {317 -- 318}, publisher = {Springer Nature}, title = {{Mitochondrial DNA: new clues about evolution}}, doi = {10.1038/306317a0}, volume = {306}, year = {1983}, } @article{3666, abstract = {We have made an extensive allozyme survey of 21 enzyme and protein loci in populations of the alpine grasshopper Podisma pedestris. This species occurs in two races, differing by a chromosomal fusion which separates the ancestral XO/XX race from a derived neo-XY race. These races also differ in DNA content, and hybrids between them have reduced viability. Electrophoresis reveals that the amount of genetic differentiation between these races is no greater than the variation among populations within each race. Both larger-scale surveys and a detailed survey of an area where the races hybridize, show that the chromosomal change is not correlated with gene frequency changes at any of the 21 loci studied. These findings are consistent with recently developed theory concerning the strength of the barrier to gene flow posed by a hybrid zone with characteristics such as those measured experimentally in Podisma. It is argued that hybrid zones in other species which involve allozymic differences do so because of stronger selection against hybrids rather than through mating isolation.}, author = {Halliday, Bruce and Barton, Nicholas H and Hewitt, Godfrey}, issn = {1095-8312}, journal = {Biological Journal of the Linnean Society}, keywords = {Hybrid zone, Electrophoresis, Podisma pedestris, Polymorphism}, number = {1}, pages = {51 -- 62}, publisher = {Oxford University Press}, title = {{Electrophoretic analysis of a chromosomal hybrid zone in the grasshopper Podisma pedestris}}, doi = {10.1111/j.1095-8312.1983.tb00776.x}, volume = {19}, year = {1983}, } @article{3667, abstract = {Populations of the grasshopper Podisma pedestris were collected from two ends of a zone of hybridization between two chromosome races, at Seyne and Tende in southern France. 21 enzyme and protein loci were detected by gel electrophoresis. Six of these loci showed widespread polymorphism, and a further eleven had very little or no variation. Two loci (Idh, 6Pgd) had rare alleles in different frequencies in the two areas surveyed. The remaining two loci (Mdh-1, Mdh-2) showed a marked increase in the frequency of rare variants, from 1 per cent outside the hybrid zone, up to 5 per cent at its centre. This region of increased electrophoretic variation coincided with the chromosomal cline between the two races, and with a region of decreased viability. It was spread over about the same width as the chromosomal cline. Possible explanations for this extra variation include intragenic recombination and elevated mutation rates.}, author = {Barton, Nicholas H and Halliday, Bruce and Hewitt, Godfrey}, issn = {1365-2540}, journal = {Heredity}, number = {2}, pages = {139 -- 146}, publisher = {Nature Publishing Group}, title = {{Rare electrophoretic variants in a hybrid zone}}, doi = {10.1038/hdy.1983.15}, volume = {50}, year = {1983}, } @article{3668, abstract = {When two populations which differ at many loci meet, the degree of introgression of alleles across the boundary will depend on the selection acting on each locus (s), the rate of recombination between adjacent loci (r), and the number of loci involved (n). Simple scaling arguments suggest that the behavior of the system should depend on the ratio of selection to recombination (θ = s/r), and on n. This is borne out by mathematical analysis of two demes which exchange individuals at a low rate; when selection is stronger than recombination (θ > 1), the effective selection on each locus is comparable to the total selection over the whole genome (s* ∼ ns). When selection is weaker than recombination (θ < 1), the effective selection is much weaker, but is still stronger than the selection on each locus alone (s* \sim sn20 for small θ). When n is very large, these two regimes are separated by a sharp threshold at θ = 1. The results are extended to two taxa which meet in a continuous habitat; the effective selection pressure, which determines the width of the hybrid zone, behaves in the same way as for the simpler case above. Even when selection is weak compared to recombination, multilocus clines have a sharp step at their center, flanked by tails of introgression in which the alleles behave independently of each other. The set of clines acts as a barrier to gene flow, and it is shown that the barrier is strongest when selection is spread over many loci. The implications of the results for divergence and speciation are discussed.}, author = {Barton, Nicholas H}, issn = {1558-5646}, journal = {Evolution; International Journal of Organic Evolution}, number = {3}, pages = {454 -- 471}, publisher = {Society for the Study of Evolution}, title = {{Multilocus clines}}, doi = {10.2307/2408260}, volume = {37}, year = {1983}, }