External-Memory Algorithms for Processing Line Segments in Geographic Information Systems

The original publication is available at www.springerlink.comIn the design of algorithms for large-scale applications it is essential to consider the problem of minimizing I/O communication. Geographical information systems (GIS) are good examples of such large-scale applications as they frequently handle huge amounts of spatial data. In this paper we develop e cient new external-memory algorithms for a number of important problems involving line segments in the plane, including trapezoid decomposition, batched planar point location, triangulation, red-blue line segment intersection reporting, and general line segment intersection reporting. In GIS systems, the rst three problems are useful for rendering and modeling, and the latter two are frequently used for overlaying maps and extracting information from them

On Constant Factors in Comparison-Based Geometric Algorithms and Data Structures

Many standard problems in computational geometry have been solved asymptotically optimally as far as comparison-based algorithms are concerned, but there has been little work focusing on improving the constant factors hidden in big-Oh bounds on the number of comparisons needed. In this thesis, we consider orthogonal-type problems and present a number of results that achieve optimality in the constant factors of the leading terms, including: - An output-sensitive algorithm that computes the maxima for a set of n points in two dimensions using 1n log(h) + O(n sqrt(log(h))) comparisons, where h is the size of the output. - A randomized algorithm that computes the maxima in three dimensions that uses 1n log(n) + O(n sqrt(log(n))) expected number of comparisons. - A randomized output-sensitive algorithm that computes the maxima in three dimensions that uses 1n log(h) + O(n log^(2/3)(h)) expected number of comparisons, where h is the size of the output. - An output-sensitive algorithm that computes the convex hull for a set of n points in two dimensions using 1n log(h) + O(n sqrt(log(h))) comparisons and O(n sqrt(log(h))) sidedness tests, where h is the size of the output. - A randomized algorithm for detecting whether of a set of n horizontal and vertical line segments in the plane intersect that uses 1n log(n) +O(n sqrt(log(n))) expected number of comparisons. - A data structure for point location among n axis-aligned disjoint boxes in three dimensions that answers queries using at most (3/2)log(n)+ O(log(log(n))) comparisons. The data structure can be extended to higher dimensions and uses at most (d/2)log(n)+ O(log(log(n))) comparisons. - A data structure for point location among n axis-aligned disjoint boxes that form a space-filling subdivision in three dimensions that answers queries using at most (4/3)log(n)+ O(sqrt(log(n))) comparisons. The data structure can be extended to higher dimensions and uses at most ((d+1)/3)log(n)+ O(sqrt(log(n))) comparisons. Our algorithms and data structures use a variety of techniques, including Seidel and Adamy's planar point location method, weighted binary search, and height-optimal BSP trees

Computational geometry through the information lens

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 111-117).This thesis revisits classic problems in computational geometry from the modern algorithmic perspective of exploiting the bounded precision of the input. In one dimension, this viewpoint has taken over as the standard model of computation, and has led to a powerful suite of techniques that constitute a mature field of research. In two or more dimensions, we have seen great success in understanding orthogonal problems, which decompose naturally into one dimensional problems. However, problems of a nonorthogonal nature, the core of computational geometry, have remained uncracked for many years despite extensive effort. For example, Willard asked in SODA'92 for a o(nlg n) algorithm for Voronoi diagrams. Despite growing interest in the problem, it was not successfully solved until this thesis. Formally, let w be the number of bits in a computer word, and consider n points with O(w)-bit rational coordinates. This thesis describes: * a data structure for 2-d point location with O(n) space, and 0( ... )query time. * randomized algorithms with running time 9 ... ) for 3-d convex hull, 2-d Voronoi diagram, 2-d line segment intersection, and a variety of related problems. * a data structure for 2-d dynamic convex hull, with O ( ... )query time, and O ( ... ) update time. More generally, this thesis develops a suite of techniques for exploiting bounded precision in geometric problems, hopefully laying the foundations for a rejuvenated research direction.by Mihai Pǎtraşcu.S.M

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Photopoetry and the Bioscopic Book: Russian and Czech Avant-Garde Experiments of the 1920s.

This dissertation focuses on three select examples of avant-garde poetry books—Mayakovsky’s and Rodchenko’s "About This" (1923), Mayakovsky’s and Rozhkov’s "To the Workers of Kursk" (1924-7) and Nezval and Teige’s "Alphabet" (1926), all illustrated by photomontages or diverse techniques involving photographic material. By way of three distinct case studies, it examines the avant-garde photo-poetry works from the angle of the bioscopic book, a concept envisaged in a programmatic manner by El Lissitzky in 1923. Through historically contextualized close readings, the analysis proposes that the 1920s bioscopic book should be understood as a theoretical, if not visionary, concept of a visual technology approximated in the series of experiments within the avant-garde photo-poetry genre. The dissertation conceptualizes the bioscopic book as an alternative cinematic apparatus through examining its materiality and dynamic conceptual design. By elaborating on different avant-garde “programs,” embodied in the medium’s conceptual design, the analysis demonstrates how these three selected examples, despite being differently designed apparatuses, all invite the reader/viewer to operate as a producer by joining the collective authorship of the poet and graphic designer in conducting perpetual transfer from one medium to another. In managing such interpretative transduction from one semiotic system to another, this dissertation argues, the reader/viewer both takes part in the topography of the bioscopic book and becomes a part of its conceptual-material circuit. The reader/viewer participates in the re-creation of the cinematic “projection” by setting the alternating current of the bioscopic book in motion. I argue that the bioscopic book is a technology “programmed” to function as a “suggestion apparatus” for a two-way communication between the different media and the reader/viewer, who herself becomes a channel, a medium, an active “influencing machine,” a prosumer. The dissertation offers a theory of the bioscopic book concept as a technology for 1) the formulation and re-production of “montage thinking” as a new cognitive model by which we interact with the outside world, 2) the augmentation of intermedial and interpersonal dialogue, and 3) the transformation of readers/viewers into prosumers.PhDSlavic Languages & LiteraturesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/100092/1/aboskov_1.pd