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Enclosing K Points in the Smallest Axis Parallel Rectangle
, 1998
"... We consider the following clustering problem. Given a set S of n points in the plane, and given an integer k, n 2 ! k n, we want to find the smallest axis parallel rectangle (smallest perimeter or area) that encloses exactly k points of S. We present an algorithm which runs in time O(n + k(n \Ga ..."
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We consider the following clustering problem. Given a set S of n points in the plane, and given an integer k, n 2 ! k n, we want to find the smallest axis parallel rectangle (smallest perimeter or area) that encloses exactly k points of S. We present an algorithm which runs in time O(n + k
Journal of Emerging Trends in Computing and Information Sciences c©20092012 CIS Journal. All rights reserved. Smallest axisparallel rectangle enclosing at least k points
"... Let P be a set of n points on a twodimensional plane. In this work, we present an algorithm that identifies a smallest area axisparallel rectangle enclosing at least k points of P (1 < k ≤ n). The worst case time and space complexities of the algorithm are O(n4) and O(n2) respectively. ..."
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Let P be a set of n points on a twodimensional plane. In this work, we present an algorithm that identifies a smallest area axisparallel rectangle enclosing at least k points of P (1 < k ≤ n). The worst case time and space complexities of the algorithm are O(n4) and O(n2) respectively.
Deterministic Rectangle Enclosure and Offline Dominance Reporting on the RAM
"... Abstract. We revisit a classical problem in computational geometry that has been studied since the 1980s: in the rectangle enclosure problem we want to report all k enclosing pairs of n input rectangles in 2D. We present the first deterministic algorithm that takes O(n logn + k) worstcase time and ..."
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Abstract. We revisit a classical problem in computational geometry that has been studied since the 1980s: in the rectangle enclosure problem we want to report all k enclosing pairs of n input rectangles in 2D. We present the first deterministic algorithm that takes O(n logn + k) worstcase time
Width Function of Curved Objects in Space and Optimal Bounding Boxes
, 1994
"... . We study the width function of piecewise smooth algebraic surface patches  that function which relates the distance between the closest pair of parallel planes enclosing the object to the direction of this pair of planes. The construction of this piecewise smooth function arises from problems i ..."
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enclosing kgon of a convex planar region bounded by algebraic curve segments, over all k gons whose corresponding inner angles are equal, where N is the number of smooth edges. In particular this includes optimizing over all triangles similar to a given one, or over all rectangles at different
A Numerical Study of the Lorenz and LorenzStenflo Systems
"... ges till offentlig granskning för avläggande av teknologie doktorsexamen fredagen ..."
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ges till offentlig granskning för avläggande av teknologie doktorsexamen fredagen
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"... ACKNOWLEDGMENTS I would like to give many thanks to Dr. Shengli Fu and Dr. Yan Huang as my advi ..."
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ACKNOWLEDGMENTS I would like to give many thanks to Dr. Shengli Fu and Dr. Yan Huang as my advi
Multiloop Position Analysis via Iterated Linear Programming
"... Abstract — This paper presents a numerical method able to isolate all configurations that an arbitrary loop linkage can adopt, within given ranges for its degrees of freedom. The procedure is general, in the sense that it can be applied to single or multiple intermingled loops of arbitrary topology. ..."
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Abstract — This paper presents a numerical method able to isolate all configurations that an arbitrary loop linkage can adopt, within given ranges for its degrees of freedom. The procedure is general, in the sense that it can be applied to single or multiple intermingled loops of arbitrary topology. It is also complete, meaning that all possible solutions get accurately bounded, irrespectively of whether the analyzed linkage is rigid or mobile. The problem is tackled by formulating a system of linear, parabolic, and hyperbolic equations, which is here solved by a new strategy exploiting its structure. The method is conceptually simple, geometric in nature, and easy to implement, yet it provides solutions at the desired accuracy in short computation times. I.
Multiloop Position Analysis via Iterated Linear Programming
"... Abstract — This paper presents a numerical method able to isolate all configurations that an arbitrary loop linkage can adopt, within given ranges for its degrees of freedom. The procedure is general, in the sense that it can be applied to single or multiple intermingled loops of arbitrary topology, ..."
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Abstract — This paper presents a numerical method able to isolate all configurations that an arbitrary loop linkage can adopt, within given ranges for its degrees of freedom. The procedure is general, in the sense that it can be applied to single or multiple intermingled loops of arbitrary topology, and complete, in the sense that all possible solutions get accurately bounded, irrespectively of whether the analyzed linkage is rigid or mobile. The problem is tackled by formulating a system of linear, parabolic, and hyperbolic equations, which is here solved by a new strategy exploiting its structure. The method is conceptually simple, geometric in nature, and easy to implement, yet it provides solutions at the desired accuracy in short computation times. I.
INSTITUT DE ROB `OTICA I INFORM `ATICA INDUSTRIAL PREPRINT 1 A BranchandPrune Solver for Distance Constraints
"... Abstract — Given some geometric elements such as points and lines in , subject to a set of pairwise distance constraints, the problem tackled in this paper is that of finding all possible configurations of these elements that satisfy the constraints. Many problems in Robotics (such as the position ..."
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Abstract — Given some geometric elements such as points and lines in , subject to a set of pairwise distance constraints, the problem tackled in this paper is that of finding all possible configurations of these elements that satisfy the constraints. Many problems in Robotics (such as the position analysis of serial and parallel manipulators) and CAD/CAM (such as the interactive placement of objects) can be formulated in this way. The strategy herein proposed consists in looking for some of the a priori unknown distances, whose derivation permits solving the problem rather trivially. Finding these distances relies on a branchandprune technique that iteratively eliminates from the space of distances entire regions which cannot contain any solution. This elimination is accomplished by applying redundant necessary conditions derived from the theory of Distance Geometry. The experimental results qualify this approach as a promising one. Index Terms — Kinematic and geometric constraint solving, distance constraint, CayleyMenger determinant, branchandprune, interval method, direct and inverse kinematics, octahedral manipulator. I.
Automatic Enumeration of (Relatedkey) Differential and Linear Characteristics with Predefined Properties and Its Applications
"... Abstract. In this paper, we investigate the Mixedinteger Linear Programming (MILP) modelling of the differential and linear behavior of a wide rang of block ciphers. The differential and linear behavior of the transformations involved in a block cipher can be described by a set P ⊆ {0, 1}n ⊆ Rn. We ..."
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Abstract. In this paper, we investigate the Mixedinteger Linear Programming (MILP) modelling of the differential and linear behavior of a wide rang of block ciphers. The differential and linear behavior of the transformations involved in a block cipher can be described by a set P ⊆ {0, 1}n ⊆ Rn. We show that P is exactly the set of all 01 solutions of the Hrepresentation of the convex hull of P. In addition, we can find a small number of inequalities in the Hrepresentation of the convex hull of P such that the set of all 01 solutions of these inequalities equals P. Based on these discoveries and MILP technique, we propose an automatic method for finding high probability (relatedkey) differential or linear characteristics of block ciphers. Compared with Sun et al.’s heuristic method presented in Asiacrypt 2014, the new method is exact for most ciphers in the sense that every feasible 01 solution of the MILP model generated by the new method corresponds to a valid characteristic, and therefore there is no need to repeatedly add valid cuttingoff inequalities into the MILP model as is done in Sun et al.’s method; the new method is more powerful which allows us to get the exact lower bounds of the number of differentially or linearly active Sboxes; and the new method is more efficient which is able to obtain characteristic enjoying higher probability or covering more rounds of a cipher with less computational effort.
Results 1  10
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