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Universal Limit Laws for Depths in Random Trees
 SIAM Journal on Computing
, 1998
"... Random binary search trees, bary search trees, medianof(2k+1) trees, quadtrees, simplex trees, tries, and digital search trees are special cases of random split trees. For these trees, we o#er a universal law of large numbers and a limit law for the depth of the last inserted point, as well as a ..."
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Cited by 50 (8 self)
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Random binary search trees, bary search trees, medianof(2k+1) trees, quadtrees, simplex trees, tries, and digital search trees are special cases of random split trees. For these trees, we o#er a universal law of large numbers and a limit law for the depth of the last inserted point, as well as a law of large numbers for the height.
Shapes And Implementations In ThreeDimensional Geometry
, 1993
"... Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is often useful or required to compute what one might call the "shape" of the set. For that purpose, this thesis deals with the formal notion of the family of alpha shapes of a finite point set in th ..."
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Cited by 37 (5 self)
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Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is often useful or required to compute what one might call the "shape" of the set. For that purpose, this thesis deals with the formal notion of the family of alpha shapes of a finite point set in three dimensional space. Each shape is a welldefined polytope, derived from the Delaunay triangulation of the point set, with a real parameter controlling the desired level of detail. Algorithms and data structures are presented that construct and store the entire family of shapes, with a quadratic time and space complexity, in the worst case.
NicheWorks—interactive visualization of very large graphs
 Proceedings of Graph Drawing ’97
, 1997
"... The difference between displaying networks with 100–1,000 nodes and displaying ones with 10,000–100,000 nodes is not merely quantitative, it is qualitative. Layout algorithms suitable for the former are too slow for the latter, requiring new algorithms or modified (often relaxed) versions of existin ..."
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Cited by 10 (0 self)
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The difference between displaying networks with 100–1,000 nodes and displaying ones with 10,000–100,000 nodes is not merely quantitative, it is qualitative. Layout algorithms suitable for the former are too slow for the latter, requiring new algorithms or modified (often relaxed) versions of existing algorithms to be invented. The density of nodes and edges displayed per inch of screen real estate requires special visual techniques to filter the graphs and focus attention. Compounding the problem is that large reallife networks are often weighted graphs and usually have additional data associated with the nodes and edges. A system for investigating and exploring such large, complex datasets needs to be able to display both graph structure and node and edge attributes so that patterns and information hidden in the data can be seen. In this article we describe a tool that addresses these needs, the NicheWorks tool. We describe and comment on the available layout algorithms and the linked views interaction system, and detail two examples of the use of NicheWorks for analyzing Web sites and detecting international telephone fraud.
A Framework for PhysicallyBased Information Visualization
, 1997
"... The following paper describes a framework for the visualization and analysis of economic data. It can be employed in the context of risk analysis, stock prediction and other tasks being important in the context of banking. The system bases on a quantification of the similarity of related objects, wh ..."
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Cited by 9 (3 self)
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The following paper describes a framework for the visualization and analysis of economic data. It can be employed in the context of risk analysis, stock prediction and other tasks being important in the context of banking. The system bases on a quantification of the similarity of related objects, which governs the parameters of a massspring system, organized as two concentric spheres. More specifically, we initialize all information units onto the surface of the inner sphere and attach them with springs to the outer sphere. Since the spring stiffnesses correspond to the computed similarity measures, the system converges into an energy minimum, which reveals multidimensional relations and adjacencies in terms of spatial neighborhoods. In order to simplify complex setups we propose an additional clustering algorithm for postprocessing. Furthermore, depending on the application scenario we support different topologic arrangements of related objects. In addition, we implemented various interaction techniques allowing semantic analysis of the underlying data sets. The versatility of our approach is illustrated by two examples, namely a comparison of agricultural productivity and an analysis of the relation between interest rates and other economic data.
Certification Trails and Software Design for Testability
 Proceedings of the 1993 International Test Conference
, 1993
"... This paper investigates design techniques which may be applied to make program testing easier. We present methods for modifying a program to generate additional data which we refer to as a certification trail. This additional data is designed to allow the program output to be checked more quickly an ..."
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Cited by 4 (3 self)
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This paper investigates design techniques which may be applied to make program testing easier. We present methods for modifying a program to generate additional data which we refer to as a certification trail. This additional data is designed to allow the program output to be checked more quickly and effectively. Certification trails [14, 16] have heretofore been described primarily from a theoretical perspective. In this paper, we report on a comprehensive attempt to assess experimentally the performance and overall value of the certification trail method. The method has been applied to nine fundamental, wellknown algorithms for the following problems: convex hull, sorting, huffman tree, shortest path, closest pair, line segment intersection, longest increasing subsequence, skyline, and voronoi diagram. Runtime performance data for each of these problems is given, and selected problems are described in more detail. Our results indicate that there are many cases in which certificatio...
The Point in Polygon Problem for Arbitrary Polygons
, 2001
"... A detailed discussion of the point in polygon problem for arbitrary polygons is given. Two concepts for solving this problem are known in literature: the evenodd rule and the winding number, the former leading to raycrossing, the latter to angle summation algorithms. First we show by mathematical ..."
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Cited by 3 (0 self)
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A detailed discussion of the point in polygon problem for arbitrary polygons is given. Two concepts for solving this problem are known in literature: the evenodd rule and the winding number, the former leading to raycrossing, the latter to angle summation algorithms. First we show by mathematical means that both concepts are very closely related, thereby developing a first version of an algorithm for determining the winding number. Then we examine how to accelerate this algorithm and how to handle special cases. Furthermore we compare these algorithms with those found in literature and discuss the results. 2001 Elsevier Science B.V. All rights reserved.
Data Structures
 ACM Computer Surveys
, 1996
"... Introduction The study of data structures, i.e., methods for organizing data that are suitable for computer processing, is one of the classic topics of computer science. At the hardware level, a computer views storage devices such as internal memory and disk as holders of elementary data units (byt ..."
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Cited by 1 (0 self)
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Introduction The study of data structures, i.e., methods for organizing data that are suitable for computer processing, is one of the classic topics of computer science. At the hardware level, a computer views storage devices such as internal memory and disk as holders of elementary data units (bytes), each accessible through its address (an integer). When writing programs, instead of manipulating the data at the byte level, it is convenient to organize them into higher level entities, called data structures. Most data structures can be viewed as containers that store a collection of objects of a given type, called the elements of the container. Often a total order is defined among the elements (e.g., alphabetically ordered names, points in the plane ordered by xcoordinate). A data structure has an associated repertory of operations, classified into queries, which retrieve information on the dat
On Topological Diversity and Multiple Path Planning
"... Conventional robot path planning aims at finding a single best path for a robot to perform a task according to certain optimization criteria. However, as a robot operates in a real environment with uncertainties, it is often desirable and even necessary for the robot to know alternative feasible pat ..."
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Conventional robot path planning aims at finding a single best path for a robot to perform a task according to certain optimization criteria. However, as a robot operates in a real environment with uncertainties, it is often desirable and even necessary for the robot to know alternative feasible paths so that it can deal with unknowns or changes in both the environment and the task effectively and efficiently. In this paper, we discuss how to define representative paths based on the concept of topological diversity in a continuous space and describe the search of such topologically diverse paths by an Evolutionary Planner/Navigator (EP/N) based on techniques of evolutionary computation. 1 Introduction The path planning problem for a robot is typically formulated as follows: given a robot and a description of an environment, plan a single path of the robot between two specified locations, which is collisionfree and satisfies certain optimization criteria. However, as a robot operates...