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  • 11
    Electronic Resource
    Electronic Resource
    Springer
    Algorithmica 13 (1995), S. 325-345 
    ISSN: 1432-0541
    Keywords: Arrangements ; Cuttings ; Range-searching ; Dynamization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider the half-space range-reporting problem: Given a setS ofn points in ℝd, preprocess it into a data structure, so that, given a query half-space γ, allk points ofS ∩ γ can be reported efficiently. We extend previously known static solutions to dynamic ones, supporting insertions and deletions of points ofS. For a given parameterm,n ≤m ≤n ⌊d/2⌋ and an arbitrarily small positive constant ɛ, we achieveO(m 1+ɛ) space and preprocessing time, O((n/m ⌊d/2⌋ logn+k) query time, and O(m1+ɛn) amortized update time (d ≳ 3). We present, among others, the following applications: an O(n1+ɛ)-time algorithm for computing convex layers in ℝ3, and an output sensitive algorithm for computing a level in an arrangements of planes in ℝ3, whose time complexity is O((b+n) nɛ, whereb is the size of the level.
    Type of Medium: Electronic Resource
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  • 12
    Electronic Resource
    Electronic Resource
    Springer
    Algorithmica 15 (1996), S. 626-660 
    ISSN: 1432-0541
    Keywords: Arrangements ; Data structures ; Intersection searching ; Partition trees
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Efficient data structures are given for the following two query problems: (i) preprocess a setP of simple polygons with a total ofn edges, so that all polygons ofP intersected by a query segment can be reported efficiently, and (ii) preprocess a setS ofn segments, so that the connected components of the arrangement ofS intersected by a query segment can be reported quickly. In these problems we do not want to return the polygons or connected components explicitly (i.e., we do not wish to report the segments defining the polygon, or the segments lying in the connected components). Instead, we assume that the polygons (or connected components) are labeled and we just want to report their labels. We present data structures of sizeO(n 1+ε) that can answer a query in timeO(n 1+ε+k), wherek is the output size. If the edges ofP (or the segments inS) are orthogonal, the query time can be improved toO(logn+k) usingO(n logn) space. We also present data structures that can maintain the connected components as we insert new segments. For arbitrary segments the amortized update and query time areO(n 1/2+ε) andO(n 1/2+ε+k), respectively, and the space used by the data structure isO(n 1+ε. If we allowO(n 4/3+ε space, the amortized update and query time can be improved toO(n 1/3+ε andO(n 1/3+ε+k, respectively. For orthogonal segments the amortized update and query time areO(log2 n) andO(log2 n+klogn), and the space used by the data structure isO (n logn). Some other related results are also mentioned.
    Type of Medium: Electronic Resource
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  • 13
    Electronic Resource
    Electronic Resource
    Springer
    Discrete & computational geometry 21 (1999), S. 373-388 
    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
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  • 14
    Electronic Resource
    Electronic Resource
    Springer
    Discrete & computational geometry 19 (1998), S. 315-331 
    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
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  • 15
    Electronic Resource
    Electronic Resource
    Springer
    Discrete & computational geometry 22 (1999), S. 201-221 
    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
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  • 16
    Electronic Resource
    Electronic Resource
    Springer
    Discrete & computational geometry 19 (1998), S. 95-104 
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We show that the largest similar copy of a convex polygon P with m edges inside a convex polygon Q with n edges can be computed in O(mn 2 log n) time. We also show that the combinatorial complexity of the space of all similar copies of P inside Q is O(mn 2 ) , and that it can also be computed in O(mn 2 log n) time.
    Type of Medium: Electronic Resource
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  • 17
    Electronic Resource
    Electronic Resource
    Springer
    Discrete & computational geometry 20 (1998), S. 287-305 
    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
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  • 18
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Letters Edition 24 (1986), S. 581-586 
    ISSN: 0887-6258
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 19
    Electronic Resource
    Electronic Resource
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 25 (1987), S. 839-854 
    ISSN: 0887-6266
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The preparation, rheology, and mechanical properties of a family of blends composed of transition-metal neutralized sulfonated ethylene-propylene-diene elastomers (S-EPDM) and styrene-4 vinylpyridine copolymers (SVP) are described. These polymeric materials contain relatively low levels of interacting groups (≤ 10 mol%), which are, however, sufficient for forming an intermolecular complex. A distinguishing characteristic of these blends is that the rheology and mechanical properties are strongly influenced by a coordination-type bonding between the transition metal and the basic nitrogen unit. As a result, markedly improved and enhanced physical properties are observed, especially when the stoichometric ratio of the interacting moieties are approached (SO3-/N = 1/1). This enhancement in properties is clearly exhibited in melt viscosity data, dynamic mechanical data, and thermal data. The blend morphology is also altered by complex formation, as is observed in scanning electron microscopy of the blends from which one of the ingredients was selectively extracted. At the stoichometric ratio, the blend of the olefinic elastomeric ionomer and the styrenic thermoplastic copolymer approaches a single-phase system. Such blends are otherwise completely immiscible when the coordination-type interacting groups are absent from either of the individual components. Accordingly, it was observed that nontransition-type (Na, Mg) counterions have only a marginal effect on the compatibility of these blends, as is the case in the completely unfunctionized blend components.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 20
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Physics Edition 23 (1985), S. 1869-1881 
    ISSN: 0098-1273
    Keywords: Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Far-infrared spectra of a series of un-neutralized and neutralized lightly sulfonated polystyrenes with varying sulfonation levels have been investigated to seek spectroscopic evidence for microphase separation known to control the physical properties of these polymers. Broad, strong absorbance bands, not found in the spectrum of unmodified polystyrene, are observed in the spectra of the sulfonated analogs. The effects on the far-infrared spectra both of sulfonation level and of the mass and charge of the neutralizing cation are discussed in terms of cation motion and the formation of ion-rich domains.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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