Results 1  10
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334
Reverse Search for Enumeration
 Discrete Applied Mathematics
, 1993
"... The reverse search technique has been recently introduced by the authors for efficient enumeration of vertices of polyhedra and arrangements. In this paper, we develop this idea in a general framework and show its broader applications to various problems in operations research, combinatorics, and ..."
Abstract

Cited by 205 (26 self)
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The reverse search technique has been recently introduced by the authors for efficient enumeration of vertices of polyhedra and arrangements. In this paper, we develop this idea in a general framework and show its broader applications to various problems in operations research, combinatorics
Topology and arrangement computation of semialgebraic planar curves
 CAGD
, 2008
"... We describe a new subdivision method to efficiently compute the topology and the arrangement of implicit planar curves. We emphasize that the output topology and arrangement are guaranteed to be correct. Although we focus on the implicit case, the algorithm can also treat parametric or piecewise lin ..."
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Cited by 13 (3 self)
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We describe a new subdivision method to efficiently compute the topology and the arrangement of implicit planar curves. We emphasize that the output topology and arrangement are guaranteed to be correct. Although we focus on the implicit case, the algorithm can also treat parametric or piecewise
Hyperplane arrangements: at the crossroads of topology and combinatorics
 COLLOQUIUM TALK AT GOETHE UNIVERSITY FRANKFURT, GERMANY
, 2013
"... Much of the fascination with arrangements of complex
hyperplanes comes from the rich interplay between the combinatorics
of the intersection lattice and the algebraic topology of the
complement. A key bridge between the two is provided
by the resonance varieties of the cohomology ring and by
..."
Abstract
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Much of the fascination with arrangements of complex
hyperplanes comes from the rich interplay between the combinatorics
of the intersection lattice and the algebraic topology of the
complement. A key bridge between the two is provided
by the resonance varieties of the cohomology ring
Complex Arrangements: Algebra, Geometry, Topology
, 2006
"... A hyperplane arrangement A is a finite collection of hyperplanes in some fixed (typically real or complex) vector space V. For simplicity, in this overview we work over the complex numbers C. There is a host of beautiful mathematics associated to the complement X = V A. Perhaps the first interesting ..."
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Cited by 2 (2 self)
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is the fundamental group; unlike the cohomology ring, π1(X) is not determined by L(A). In [15], Hirzebruch wrote ”The topology of the complement of an arrangement of lines in P 2 is very interesting, the investigation of the fundamental group very difficult. ” For any group G, the lower central series is a chain
Rounding Arrangements Dynamically
, 1995
"... We describe a robust, dynamic algorithm to compute the arrangement of a set of line segments in the plane, and its implementation. The algorithm is robust because, following Greene 1 and Hobby, 2 it rounds the endpoints and intersections of all line segments to representable points, but in a ..."
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Cited by 41 (2 self)
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We describe a robust, dynamic algorithm to compute the arrangement of a set of line segments in the plane, and its implementation. The algorithm is robust because, following Greene 1 and Hobby, 2 it rounds the endpoints and intersections of all line segments to representable points, but in a
Jacobi Curves: Computing the Exact Topology of Arrangements of NonSingular Algebraic Curves
 IN ESA 2003, LNCS 2832
, 2000
"... We present an approach that extends the BentleyOttmann sweepline algorithm [3] to the exact computation of the topology of arrangements induced by nonsingular algebraic curves of arbitrary degrees. Algebraic ..."
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Cited by 9 (3 self)
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We present an approach that extends the BentleyOttmann sweepline algorithm [3] to the exact computation of the topology of arrangements induced by nonsingular algebraic curves of arbitrary degrees. Algebraic
Arrangement Computation for Planar Algebraic Curves
, 2011
"... We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometrictopological analysis of the decomposition of the plane induced by a finite number of algebraic curves in terms of a cylindrical algebraic decomposition of the ..."
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Cited by 2 (2 self)
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We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometrictopological analysis of the decomposition of the plane induced by a finite number of algebraic curves in terms of a cylindrical algebraic decomposition
Hierarchical structure in financial markets
 Eur. Phys. J. B
, 1999
"... I find a topological arrangement of stocks traded in a financial market which has associated a meaningful economic taxonomy. The topological space is a graph connecting the stocks of the portfolio analyzed. The graph is obtained starting from the matrix of correlation coefficient computed between al ..."
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Cited by 124 (2 self)
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I find a topological arrangement of stocks traded in a financial market which has associated a meaningful economic taxonomy. The topological space is a graph connecting the stocks of the portfolio analyzed. The graph is obtained starting from the matrix of correlation coefficient computed between
Puzzle Piece Topology: Detecting Arrangements in Smart Object Interfaces, to appear
 in Proceedings of WSGS ‘99 (Czech Republic
, 1999
"... Smart object interfaces enable a computer to respond to a group of users ’ manipulations of a physical environment. This unobtrusive interface is especially well suited for providing guidance as students attempt to solve mathematical and scientific puzzles. This paper introduces a formalism for desc ..."
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Cited by 2 (1 self)
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for describing arrangements of smart objects on a 2D surface, and suggests a strategy for efficiently representing such arrangements in a computer application. It then shows how these techniques are implemented in a Tangram with a smart objects interface, which provides multimedia feedback as children play
General Lexicographic Shellability And Orbit Arrangements
 Ann. of Comb
, 1996
"... We introduce a new poset property which we call ECshellability. It is more general than the more established concept of ELshellability, but still implies shellability. Because of the Theorem 3.10 ECshellability is entitled to be called general lexicographic shellability. As an application of ..."
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Cited by 18 (4 self)
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of our new concept, we prove that intersection lattices \Pi of orbit arrangements A are ECshellable for a very large class of partitions . This allows to compute the topology of the link and the complement for these arrangements. In particular, for this class of 's, we are able to settle a
Results 1  10
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334