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Topological sweep in degenerate cases
 in Proceedings of the 4th Workshop on Algorithm Engineering and Experiments (ALENEX’02
, 2002
"... Abstract. Topological sweep can contribute to efficient implementations of various algorithms for data analysis.Real data, however, has degeneracies.The modification of the topological sweep algorithm presented here handles degenerate cases such as parallel or multiply concurrent lines without requi ..."
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Abstract. Topological sweep can contribute to efficient implementations of various algorithms for data analysis.Real data, however, has degeneracies.The modification of the topological sweep algorithm presented here handles degenerate cases such as parallel or multiply concurrent lines without requiring numerical perturbations to achieve general position.Our method maintains the O(n 2) and O(n) time and space complexities of the original algorithm, and is robust and easy to implement. We present experimental results. 1
Some constrained minimax and maximin location problems
 Studies in Locational Analysis
, 2000
"... In this paper we consider constrained versions of the Euclidean minimax facility location problem. We provide an O(n+m) time algorithm for the problem of constructing the minimum enclosing circle of a set of n points with center constrained to satisfy m linear constraints. As a corollary, we obtain ..."
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Cited by 5 (2 self)
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In this paper we consider constrained versions of the Euclidean minimax facility location problem. We provide an O(n+m) time algorithm for the problem of constructing the minimum enclosing circle of a set of n points with center constrained to satisfy m linear constraints. As a corollary, we obtain a linear time algorithm for the problem when the center is constrained to lie in an mvertex convex polygon, which improves the best known solution of O((n + m) log(n + m)) time. We also consider some constrained versions of the maximin problem, namely an obnoxious facility location problem in which we are given a set of n linear constraints, each representing a halfplane where some population may live, and the goal is to locate a point such that the minimum distance to the inhabited region is maximized. We provide optimal (n) time algorithms for this problem in the plane, as well as on the sphere.
Perspective Projections and Removal of Degeneracies
 Proc. of the Tenth Canadian Conference on Computational Geometry
, 1998
"... In this paper we consider the following problems: (1) computing projections with distinct xcoordinates, (2) computing noncollinear projections, (3) computing noncocircular projections, and (4) computing projections with nonparallel line segments. Here the word projection means perspective project ..."
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Cited by 3 (3 self)
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In this paper we consider the following problems: (1) computing projections with distinct xcoordinates, (2) computing noncollinear projections, (3) computing noncocircular projections, and (4) computing projections with nonparallel line segments. Here the word projection means perspective projection, a kind of projection that has received little attention in computational geometry. These problems are relevant to nondegeneracy assumptions and to the robustness of geometric algorithms. 1
Advances in Computational Geometry for Document Analysis
 Proc., 3rd Annual Symp. Document Analysis and Information Retrieval
, 1994
"... Many problems in document image analysis can be couched in geometric terms. We outline recent advances in computational geometry that contribute to many aspects of the document analysis process and we provide pointers to a selection of the computational geometry literature where the most relevan ..."
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Many problems in document image analysis can be couched in geometric terms. We outline recent advances in computational geometry that contribute to many aspects of the document analysis process and we provide pointers to a selection of the computational geometry literature where the most relevant results can be found. 1 Introduction Document image analysis (DIA) is concerned with the automatic transfer by machine of visual twodimensional documents, most commonly consisting of printed pages from books, magazines or newspapers. Maps and engineering drawings constitute another class of common documents. The first class of problems have much in common with optical character recognition (OCR) and both with computer vision. On the other hand DIA is a special case of computer vision and therefore its special properties give rise to special subproblems such as textblock isolation and textlineorientation inference. Furthermore these special properties allow the tailoring of more gener...
Nice Perspective Projections
"... this paper we consider the problem of computing a variety of nice perspective projections of threedimensional objects such as simple polygonal chains, wireframe drawings of graphs and geometric rooted trees. These problems arise in areas such as Computer Vision, Computer Graphics, Graph Drawin ..."
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this paper we consider the problem of computing a variety of nice perspective projections of threedimensional objects such as simple polygonal chains, wireframe drawings of graphs and geometric rooted trees. These problems arise in areas such as Computer Vision, Computer Graphics, Graph Drawing, Knot Theory and Computational Geometry. 1. INTRODUCTION When we draw or plot an image of a threedimensional (3D) object on a sheet of paper, or when we use a displaying device, such as a computer graphics screen, we obtain a 2D representation that necessarily approximates the 3D object and will never capture all its properties. It is obviously desirable to make this single * The research of the rst author was supported by MECDGESSEUID PB980933. The second author was supported by MECDGESSEUID PB980933 and DURSI 1999SGR00356. Research of the third author was supported by MECDGESSEUID PB980933 and DURSI 1999SGR00162. The fou
On Degeneracies Removable by Perspective Projections
"... In this paper we are concerned with computing nondegenerate perspective projections of sets of points and line segments in threedimensional space. For sets of points we give algorithms for computing perspective projections such that (1) all points in the projection have distinct xcoordinates, (2) ..."
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In this paper we are concerned with computing nondegenerate perspective projections of sets of points and line segments in threedimensional space. For sets of points we give algorithms for computing perspective projections such that (1) all points in the projection have distinct xcoordinates, (2) all points in the projection have both distinct x and ycoordinates, (3) no three points in the projection are collinear, and (4) no four points in the projection are cocircular. For sets of line segments we present an algorithm for computing a perspective projection such that no two segments in the projection are parallel. All our algorithms have time and space complexities bounded by low degree polynomials. We also discuss the problem of removing some intrinsic degeneracies for point and line segment sets in the plane by using perspective projections.
A Survey of 3sumHard Problems
, 2004
"... The 3sum problem is defined as follows: given a set S of n integers, do ..."
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The 3sum problem is defined as follows: given a set S of n integers, do