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Infimaximal Frames  A Technique For Making Lines Look Like Segments
 INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY AND APPLICATION
, 2000
"... Many geometric algorithms that are usually formulated for points and segments generalize easily to inputs also containing rays and lines. The sweep algorithm for segment intersection is a prototypical example. Implementations of such algorithms do, in general, not extend easily. For example, ..."
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Many geometric algorithms that are usually formulated for points and segments generalize easily to inputs also containing rays and lines. The sweep algorithm for segment intersection is a prototypical example. Implementations of such algorithms do, in general, not extend easily. For example,
An Experimental Study of PolyLogarithmic FullyDynamic Connectivity Algorithms
, 2000
"... We present an experimental study of different variants of the amortized O(log² n)time fullydynamic connectivity algorithm of Holm, de Lichtenberg, and Thorup (STOC'98). The experiments build upon experiments provided by Alberts, Cattaneo, and Italiano (SODA'96) on the randomized amortized O(log³ ..."
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We present an experimental study of different variants of the amortized O(log² n)time fullydynamic connectivity algorithm of Holm, de Lichtenberg, and Thorup (STOC'98). The experiments build upon experiments provided by Alberts, Cattaneo, and Italiano (SODA'96) on the randomized amortized O(log³ n) fullydynamic connectivity algorithm of Henzinger and King (STOC'95). Our experiments shed light upon similarities and differences between the two algorithms. We also present a slightly modified version of the HenzingerKing algorithm that runs in O(log² n) time, wh...
CONSTANTWORKSPACE ALGORITHMS FOR GEOMETRIC PROBLEMS
 JOURNAL OF COMPUTATIONAL GEOMETRY
, 2011
"... Constantworkspace algorithms may use only constantly many cells of storage in addition to their input, which is provided as a readonly array. We show how to construct several geometric structures efficiently in the constantworkspace model. Traditional algorithms process the input into a suitabl ..."
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Constantworkspace algorithms may use only constantly many cells of storage in addition to their input, which is provided as a readonly array. We show how to construct several geometric structures efficiently in the constantworkspace model. Traditional algorithms process the input into a suitable data structure (like a doublyconnected edge list) that allows efficient traversal of the structure at hand. In the constantworkspace setting, however, we cannot afford to do this. Instead, we provide operations that compute the desired features on the fly by accessing the input with no extra space. The whole geometric structure can be obtained by using these operations to enumerate all the features. Of course, we must pay for the space savings by slower running times. While the standard data structure allows us to implement traversal operations in constant time, our schemes typically take linear time to read the input data in each step. We begin with two simple problems: triangulating a planar point set and finding the trapezoidal decomposition of a simple polygon. In both cases adjacent features can be enumerated in linear time per step, resulting in total quadratic running time to output the whole structure. Actually, we show that the former result carries over to the Delaunay triangulation, and hence the Voronoi diagram. This also means that we can compute the largest empty circle of a planar point set in quadratic time and constant workspace. As another application, we demonstrate how to enumerate the features of an Euclidean minimum spanning tree (EMST) in quadratic time per step, so that the whole EMST can be found in cubic time using constant workspace. Finally, we describe how to compute a shortest geodesic path between two points in a simple polygon. Although the shortest path problem in general graphs is NLcomplete [18], this constrained problem can be solved in quadratic time using only constant workspace.
Designing a Computational Geometry Algorithms Library
 Lecture Notes for Advanced School on Algorithmic Foundations of Geographic Information Systems, CISM
, 1996
"... Introduction Geometric problems arise in many areas. Computer graphics, robotics, manufacturing, and geographic information systems are some examples. Often the same geometric subproblems are to be solved. Hence a library providing solutions for core problems in geometric computing has a wide range ..."
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Introduction Geometric problems arise in many areas. Computer graphics, robotics, manufacturing, and geographic information systems are some examples. Often the same geometric subproblems are to be solved. Hence a library providing solutions for core problems in geometric computing has a wide range of applications and can be very useful. The success of LEDA [16], a library of efficient data types and algorithms, has shown that the existence of a library can make a tremendous difference for taking advanced techniques in data structures and algorithms from theory to practice. The field of computational geometry is now very close to a state where it can provide such a library of geometric algorithms. Over the past twenty years many algorithms for geometric problems have been developed by computational geometers. Many of these algorithms clearly have no direct impact for geometric computing in practice, because they are efficient compared to other solutions only for huge problem i
What Do We Learn from Experimental Algorithmics?
 In Mathematical Foundations of Computer Science
, 2000
"... Experimental Algorithmics is concerned with the design, implementation, tuning, debugging and performance analysis of computer programs for solving algorithmic problems. It provides methodologies and tools for designing, developing and experimentally analyzing efficient algorithmic codes and aim ..."
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Experimental Algorithmics is concerned with the design, implementation, tuning, debugging and performance analysis of computer programs for solving algorithmic problems. It provides methodologies and tools for designing, developing and experimentally analyzing efficient algorithmic codes and aims at integrating and reinforcing traditional theoretical approaches for the design and analysis of algorithms and data structures. In this paper we survey some relevant contributions to the field of Experimental Algorithmics and we discuss significant examples where the experimental approach helped in developing new ideas, in assessing heuristics and techniques, and in gaining a deeper insight about existing algorithms. 1
SIMLAB  A Simulation Environment for Storage Area Networks
 In Workshop on Parallel and Distributed Processing (PDP
, 2001
"... In this paper, we present a simulation environment for storage area networks called SIMLAB. SIMLAB is a part of the PRESTO project, which is a joint project of the Electrical Engineering Department and the Computer Science Department of the Paderborn University. The aim of the PRESTO project is to c ..."
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In this paper, we present a simulation environment for storage area networks called SIMLAB. SIMLAB is a part of the PRESTO project, which is a joint project of the Electrical Engineering Department and the Computer Science Department of the Paderborn University. The aim of the PRESTO project is to construct a scalable and resourceefficient storage network that can support the realtime delivery of data. SIMLAB has been implemented to aid the development and verification of distributed algorithms for this storage network. However, it has been designed in such a way that it can also be used for the simulation of many other types of networking problems. SIMLAB is based on C++ and common libraries and input/output formats, which ensures that SIMLAB can be used on many different platforms. We therefore expect SIMLAB to be useful also for other people working on similar problems. 1 Introduction In the last couple of years, a dramatic increase in the need of storing huge amounts of data can...
ConstantWorkSpace Algorithm for a Shortest Path in a Simple Polygon
"... Abstract. We present two spaceefficient algorithms. First, we show how to report a simple path between two arbitrary nodes in a given tree. Using a technique called “computing instead of storing”, we can design a naive quadratictime algorithm for the problem using only constant work space, i.e., O ..."
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Abstract. We present two spaceefficient algorithms. First, we show how to report a simple path between two arbitrary nodes in a given tree. Using a technique called “computing instead of storing”, we can design a naive quadratictime algorithm for the problem using only constant work space, i.e., O(log n) bits in total for the work space, where n is the number of nodes in the tree. Then, another technique “controlled recursion” improves the time bound to O(n 1+ε) for any positive constant ε. Second, we describe how to compute a shortest path between two points in a simple ngon. Although the shortest path problem in general graphs is NLcomplete, this constrained problem can be solved in quadratic time using only constant work space. 1
Balancing Sparse Hamiltonian Eigenproblems
, 2003
"... Balancing a matrix by a simple and accurate similarity transformation can improve the performance of numerical methods for computing eigenvalues. We describe balancing strategies for a large and sparse Hamiltonian matrix H . It is first shown how to permute H to irreducible form while retaining i ..."
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Balancing a matrix by a simple and accurate similarity transformation can improve the performance of numerical methods for computing eigenvalues. We describe balancing strategies for a large and sparse Hamiltonian matrix H . It is first shown how to permute H to irreducible form while retaining its structure. This form can be used to decompose the Hamiltonian eigenproblem into smallersized problems. Next, we discuss the computation of a symplectic scaling matrix D so that the norm of D 1 HD is reduced. The considered scaling algorithm is solely based on matrixvector products and thus particularly suitable if the elements of H are not explicitly given. The merits of balancing for eigenvalue computations are illustrated by several practically relevant examples.
Colimit Library for Graph Transformations and Algebraic Development Techniques
, 1998
"... ions are defined both for objects and layers. There are several compatibility requirements for the definition of these functions. The set of objects contains a specific ?element which allows the source and target functions to be total on the set of objects. Up to now there exists no implementation ..."
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ions are defined both for objects and layers. There are several compatibility requirements for the definition of these functions. The set of objects contains a specific ?element which allows the source and target functions to be total on the set of objects. Up to now there exists no implementation of general colimits in the AGGsystem. This problem is currently fixed by the integration of the colimit library. Again we can use the colimit computation for Alpha algebras. For this purpose we have to find an Alpha representation of AGGgraphs. Here we will outline the idea. r0 r1 r2 object layer label v0 r4 r0 Item Data The picture above presents a possible Alpha type algebra for AGGgraphs. r 0 ; r 1 and r 2 correspond to the abstraction, source and target functions, r 4 represents the assignment of layers to objects and v 0 is the labelling function. Note that although not shown in the picture, since all references are total, r 1 ; r 2 and r 3 are defined also for layer. This shows ...
Trends and Developments in Computational Geometry
 Computer Graphics Forum
, 1995
"... This report discusses some trends and achievements in computational geometry during the past five years, with emphasis on problems related to computer graphics. Furthermore, a direction of research in computational geometry is discussed, which could help in bringing the fields of computational ge ..."
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This report discusses some trends and achievements in computational geometry during the past five years, with emphasis on problems related to computer graphics. Furthermore, a direction of research in computational geometry is discussed, which could help in bringing the fields of computational geometry and computer graphics closer together.