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On the Complexity of Some Geometric Problems in Unbounded Dimension
 J. SYMB. COMPUT
, 1990
"... This paper examines the complexity of several geometric problems due to unbounded dimension. The problems considered are: (i) minimum cover of points by unit cubes, (ii) minimum cover of points by unit balls, and (iii) minimum number of lines to hit a set of balls. Each of these problems is prove ..."
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Cited by 24 (0 self)
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This paper examines the complexity of several geometric problems due to unbounded dimension. The problems considered are: (i) minimum cover of points by unit cubes, (ii) minimum cover of points by unit balls, and (iii) minimum number of lines to hit a set of balls. Each of these problems
Directed VRRepresentable Graphs have Unbounded Dimension
 Lecture Notes in Computer Science LNCS #894
, 1994
"... Visibility representations of graphs map vertices to sets in Euclidean space and express edges as visibility relations between these sets. A threedimensional visibility representation that has been studied is one in which each vertex of the graph maps to a closed rectangle in R 3 and edges are ex ..."
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Cited by 6 (2 self)
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towards the positive z direction. A directed acyclic graph G has dimension d if d is the mini...
The parameterized complexity of some geometric problems in unbounded dimension
 In Proc. 4th IWPEC, volume 5917 of LNCS
"... We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension d: i) Given n points in R d, compute their minimum enclosing cylinder. ii) Given two npoint sets in R d, decide whether they can be separated by two hyperplanes. iii) Given a system o ..."
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Cited by 6 (3 self)
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We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension d: i) Given n points in R d, compute their minimum enclosing cylinder. ii) Given two npoint sets in R d, decide whether they can be separated by two hyperplanes. iii) Given a system
Directed RectangleVisibility Graphs have Unbounded Dimension
"... Visibility representations of graphs map vertices to sets in Euclidean space and express edges as visibility relations between these sets. One visibility representation in the plane that has been studied is one in which the vertices of the graph map to closed isothetic rectangles and the edges are e ..."
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rectanglevisibility graph can be directed by directing all edges towards the positive x and y directions, which yields a directed acyclic graph. A directed acyclic graph G has dimension d if d is the minimum integer such that the vertices of G can be ordered by d linear orderings, ! 1 ; : : : ; ! d
Computational Aspects of the Hausdorff Distance in Unbounded Dimension
, 2014
"... We study the computational complexity of determining the Hausdorff distance of two polytopes given in halfspace or vertexpresentation in arbitrary dimension. Subsequently, a matching problem is investigated where a convex body is allowed to be homothetically transformed in order to minimize its H ..."
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We study the computational complexity of determining the Hausdorff distance of two polytopes given in halfspace or vertexpresentation in arbitrary dimension. Subsequently, a matching problem is investigated where a convex body is allowed to be homothetically transformed in order to minimize its
Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics
 J. Geophys. Res
, 1994
"... . A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The ..."
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Cited by 782 (22 self)
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. The unbounded error growth found in the extended Kalman filter, which is caused by an overly simplified closure in the error covariance equation, is completely eliminated. Open boundaries can be handled as long as the ocean model is well posed. Wellknown numerical instabilities associated with the error
SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
, 2002
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 582 (23 self)
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available, and that the constraint gradients are sparse. We discuss
The Omega Test: a fast and practical integer programming algorithm for dependence analysis
 Communications of the ACM
, 1992
"... The Omega testi s ani nteger programmi ng algori thm that can determi ne whether a dependence exi sts between two array references, and i so, under what condi7: ns. Conventi nalwi[A m holds thati nteger programmiB techni:36 are far too expensi e to be used for dependence analysi6 except as a method ..."
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Cited by 521 (15 self)
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The Omega testi s ani nteger programmi ng algori thm that can determi ne whether a dependence exi sts between two array references, and i so, under what condi7: ns. Conventi nalwi[A m holds thati nteger programmiB techni:36 are far too expensi e to be used for dependence analysi6 except as a method of last resort for si:8 ti ns that cannot be deci:A by si[976 methods. We present evi[77B that suggests thiwi sdomi s wrong, and that the Omega testi s competi ti ve wi th approxi mate algori thms usedi n practi ce and sui table for usei n producti on compi lers. Experi ments suggest that, for almost all programs, the average ti me requi red by the Omega test to determi ne the di recti on vectors for an array pai ri s less than 500 secs on a 12 MIPS workstati on. The Omega testi based on an extensi n of Four i0Motzki var i ble eli937 ti n (aliB: r programmiA method) toi nteger programmi ng, and has worstcase exponenti al ti me complexi ty. However, we show that for manysiB7 ti ns i whi h ...
Models and issues in data stream systems
 IN PODS
, 2002
"... In this overview paper we motivate the need for and research issues arising from a new model of data processing. In this model, data does not take the form of persistent relations, but rather arrives in multiple, continuous, rapid, timevarying data streams. In addition to reviewing past work releva ..."
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Cited by 770 (19 self)
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In this overview paper we motivate the need for and research issues arising from a new model of data processing. In this model, data does not take the form of persistent relations, but rather arrives in multiple, continuous, rapid, timevarying data streams. In addition to reviewing past work relevant to data stream systems and current projects in the area, the paper explores topics in stream query languages, new requirements and challenges in query processing, and algorithmic issues.
The Systems Biology Markup Language (SBML): a medium for representation and exchange of biochemical network models
 Bioinformatics
, 2003
"... ..."
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