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  • 11
    Electronic Resource
    Electronic Resource
    Efficient Algorithms for Approximating Polygonal Chains (2000)
    Springer
    Discrete & computational geometry 23 (2000), S. 273-291 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We consider the problem of approximating a polygonal chain C by another polygonal chain C' whose vertices are constrained to be a subset of the set of vertices of C . The goal is to minimize the number of vertices needed in the approximation C' . Based on a framework introduced by Imai and Iri [25], we define an error criterion for measuring the quality of an approximation. We consider two problems. (1) Given a polygonal chain C and a parameter ɛ \geq 0 , compute an approximation of C , among all approximations whose error is at most ɛ , that has the smallest number of vertices. We present an O(n 4/3 + δ ) -time algorithm to solve this problem, for any δ 〉 0; the constant of proportionality in the running time depends on δ . (2) Given a polygonal chain C and an integer k , compute an approximation of C with at most k vertices whose error is the smallest among all approximations with at most k vertices. We present a simple randomized algorithm, with expected running time O(n 4/3 + δ ) , to solve this problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009500
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  • 12
    Electronic Resource
    Electronic Resource
    Lower Bounds for Kinetic Planar Subdivisions (2000)
    Springer
    Discrete & computational geometry 24 (2000), S. 721-733 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We revisit the notion of kinetic efficiency for noncanonically defined discrete attributes of moving data, like binary space partitions and triangulations. Under reasonable computational models, we obtain lower bounds on the minimum amount of work required to maintain any binary space partition of moving segments in the plane or any Steiner triangulation of moving points in the plane. Such lower bounds—the first to be obtained in the kinetic context—are necessary to evaluate the efficiency of kinetic data structures when the attribute to be maintained is not canonically defined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004540010060
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  • 13
    Electronic Resource
    Electronic Resource
    Line Transversals of Balls and Smallest Enclosing Cylinders in Three Dimensions (1999)
    Springer
    Discrete & computational geometry 21 (1999), S. 373-388 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We establish a near-cubic upper bound on the complexity of the space of line transversals of a collection of n balls in three dimensions, and show that the bound is almost tight, in the worst case. We apply this bound to obtain a near-cubic algorithm for computing a smallest infinite cylinder enclosing a given set of points or balls in 3-space. We also present an approximation algorithm for computing a smallest enclosing cylinder.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009427
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  • 14
    Electronic Resource
    Electronic Resource
    Motion Planning for a Convex Polygon in a Polygonal Environment (1999)
    Springer
    Discrete & computational geometry 22 (1999), S. 201-221 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We study the motion-planning problem for a convex m -gon P in a planar polygonal environment Q bounded by n edges. We give the first algorithm that constructs the entire free configuration space (the three-dimensional space of all free placements of P in Q ) in time that is near-quadratic in mn , which is nearly optimal in the worst case. The algorithm is also conceptually simple. Previous solutions were incomplete, more expensive, or produced only part of the free configuration space. Combining our solution with parametric searching, we obtain an algorithm that finds the largest placement of P in Q in time that is also near-quadratic in mn . In addition, we describe an algorithm that preprocesses the computed free configuration space so that reachability queries can be answered in polylogarithmic time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009455
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  • 15
    Electronic Resource
    Electronic Resource
    On Levels in Arrangements of Lines, Segments, Planes, and Triangles% (1998)
    Springer
    Discrete & computational geometry 19 (1998), S. 315-331 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We consider the problem of bounding the complexity of the k th level in an arrangement of n curves or surfaces, a problem dual to, and an extension of, the well-known k-set problem. Among other results, we prove a new bound, O(nk 5/3 ) , on the complexity of the k th level in an arrangement of n planes in R 3 , or on the number of k -sets in a set of n points in three dimensions, and we show that the complexity of the k th level in an arrangement of n line segments in the plane is $O(n\sqrt{k}\alpha(n/k))$ , and that the complexity of the k th level in an arrangement of n triangles in 3-space is O(n 2 k 5/6 α(n/k)) . 〈lsiheader〉 〈onlinepub〉26 June, 1998 〈editor〉Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt; 〈pdfname〉19n3p315.pdf 〈pdfexist〉yes 〈htmlexist〉no 〈htmlfexist〉no 〈texexist〉yes 〈sectionname〉 〈/lsiheader〉
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009348
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  • 16
    Electronic Resource
    Electronic Resource
    Approximation Algorithms for Minimum-Width Annuli and Shells (2000)
    Springer
    Discrete & computational geometry 24 (2000), S. 687-705 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. Let S be a set of n points in \re d . The ``roundness'' of S can be measured by computing the width ω * =ω * (S) of the thinnest spherical shell (or annulus in \re 2 ) that contains S . This paper contains two main results related to computing an approximation of ω * : (i) For d=2 , we can compute in O(n log n) time an annulus containing S whose width is at most 2ω * (S) . We extend this algorithm, so that, for any given parameter ε 〉0 , an annulus containing S whose width is at most (1+ε )ω * is computed in time O(n log n + n/ε 2 ) . (ii) For d \geq 3 , given a parameter ε 〉 0 , we can compute a shell containing S of width at most (1+ε)ω * either in time O ( n / ε d ) log ( \Delata / ω * ε ) or in time O ( n / ε d-2 ) log  n + 1 / εlog  \Delata / ω * ε , where Δ is the diameter of S .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004540010062
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  • 17
    Electronic Resource
    Electronic Resource
    The Discrete 2-Center Problem (1998)
    Springer
    Discrete & computational geometry 20 (1998), S. 287-305 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We present an algorithm for computing the discrete 2-center of a set P of n points in the plane; that is, computing two congruent disks of smallest possible radius, centered at two points of P , whose union covers P . Our algorithm runs in time O(n 4/3 log 5 n) .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009387
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  • 18
    Electronic Resource
    Electronic Resource
    Compressive myelopathy in fluorosis: MRI (1996)
    Springer
    Neuroradiology 38 (1996), S. 338-342 
    Details
    ISSN: 1432-1920
    Keywords: Magnetic resonance imaging ; Fluoride poisoning ; Ligaments ; Spinal cord compression
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We examined four patients with fluorosis, presenting with compressive myelopathy, by MRI, using spin-echo and fast low-angle shot sequences. Cord compression due to ossification of the posterior longitudinal ligament (PLL) and ligamentum flavum (LF) was demonstrated in one and ossification of only the LF in one. Marrow signal was observed in the PLL and LF in all the patients on all pulse sequences. In patients with compressive myelopathy secondary to ossification of PLL and/or LF, fluorosis should be considered as a possible cuase, especially in endemic regions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00596584
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  • 19
    Electronic Resource
    Electronic Resource
    Compressive myelopathy in fluorosis: MRI (1996)
    Springer
    Neuroradiology 38 (1996), S. 338-342 
    Details
    ISSN: 1432-1920
    Keywords: Key words Magnetic resonance imaging ; Fluoride poisoning ; Ligaments ; Spinal cord compression
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We examined four patients with fluorosis, presenting with compressive myelopathy, by MRI, using spin-echo and fast low-angle shot sequences. Cord compression due to ossification of the posterior longitudinal ligament (PLL) and ligamentum flavum (LF) was demonstrated in one and ossification of only the LF in one. Marrow signal was observed in the PLL and LF in all the patients on all pulse sequences. In patients with compressive myelopathy secondary to ossification of PLL and/or LF, fluorosis should be considered as a possible cause, especially in endemic regions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00596584
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    Paper (German National Licenses)
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  • 20
    Electronic Resource
    Electronic Resource
    Problems in distinguishing spinal tuberculosis from neoplasia on MRI (1996)
    Springer
    Neuroradiology 38 (1996), S. S97 
    Details
    ISSN: 1432-1920
    Keywords: Key words Spine ; infections ; Spine ; neoplasms ; Tuberculosis ; Computed tomography ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We reviewed MRI studies of 60 patients presenting with extradural compressive myeloradiculopathy secondary to vertebral disease to assess the imaging features which may help in differentiating tuberculous from neoplastic disease. Spin-echo T1-, proton density- and T2-weighted images were available for all patients and fast low-angle shot images with a low flip angle for 21 patients. Contrast-enhanced images were available for 28 patients. There were 41 patients with tuberculosis and 19 patients with neoplastic disease (metastases 11, lymphoma 6, plasmacytoma 1, and giant cell tumour 1). Discovertebral disease with or without involvement of the posterior arch was a feature not only of tuberculous spondylitis (30 patients) but also of metastases (6). The remaining 11 patients with tuberculosis had “atypical” involvement (vertebral body with or without posterior arch in 8 and posterior arch alone in 3) described as typical of neoplasms. This “typical” involvement was seen in metastases (5), lymphoma (6) and the 2 primary bone tumours. The presence of an abscess helped in differentiating tuberculosis from neoplasia in 22 of the 41 patients with tuberculosis and was absent in all with neoplasms. The presence of bone fragments in 16 patients (8 with and 8 without an abscess) was found to be specific for tuberculosis. In the absence of an abscess or bone fragments, image-guided biopsy is essential to establish the diagnosis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002340050930
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