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  • Steiner ratio  (3)
  • rat chromosome 12
  • Springer  (5)
  • 1
    Electronic Resource
    Electronic Resource
    A proof of the Gilbert-Pollak conjecture on the Steiner ratio (1992)
    Springer
    Algorithmica 7 (1992), S. 121-135 
    Details
    ISSN: 1432-0541
    Keywords: Steiner trees ; Spanning trees ; Steiner ratio ; Convexity ; Hexagonal trees
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract LetP be a set ofn points on the euclidean plane. LetL s(P) andL m (P) denote the lengths of the Steiner minimum tree and the minimum spanning tree onP, respectively. In 1968, Gilbert and Pollak conjectured that for anyP,L s (P)≥(√3/2)L m (P). We provide a proof for their conjecture in this paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01758755
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  • 2
    Electronic Resource
    Electronic Resource
    On Steiner minimal trees withL p distance (1992)
    Springer
    Algorithmica 7 (1992), S. 179-191 
    Details
    ISSN: 1432-0541
    Keywords: Steiner trees ; Spanning trees ; Steiner ratio ; L p distance ; Bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract LetL p be the plane with the distanced p (A 1 ,A 2 ) = (¦x 1 −x 2¦ p + ¦y1 −y 2¦p)/1p wherex i andy i are the cartesian coordinates of the pointA i . LetP be a finite set of points inL p . We consider Steiner minimal trees onP. It is proved that, for 1 〈p 〈 ∞, each Steiner point is of degree exactly three. Define the Steiner ratio ϱ p to be inf{L s (P)/L m (P)¦P⊂L p } whereL s (P) andL m (P) are lengths of the Steiner minimal tree and the minimal spanning tree onP, respectively. Hwang showed ϱ1 = 2/3. Chung and Graham proved ϱ2 〉 0.842. We prove in this paper that ϱ{∞} = 2/3 and √(√2/2)ϱ1ϱ2 ≤ ϱp ≤ √3/2 for anyp.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01758757
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  • 3
    Electronic Resource
    Electronic Resource
    Four polymorphic markers on rat chromosome 12 form a single linkage group (1993)
    Springer
    Biochemical genetics 31 (1993), S. 441-448 
    Details
    ISSN: 1573-4927
    Keywords: linkage analysis ; serine dehydratase ; plasminogen activator inhibitor ; simple sequence repeats ; microsatellites ; rat chromosome 12
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology
    Notes: Abstract Four PCR-typable polymorphic markers were mapped to rat chromosome 12 by linkage analysis of F2 intercross progeny of Fischer (F344/N) and Lewis (LEW/N) rat strains. The markers formed a single linkage group, covering 27.7 cM, with the following order and distance between markers: plasminogen activator inhibitor (Planh)—0.0 cM—phosphoenolpyruvate carboxykinase-related sequence 2 (Pepckr2)—15.4 cM—anonymous marker (D12N155)—12.3 cM—serine dehydratase (Sdh). All markers were identified and genotyped by PCR analysis of simple sequence repeats. The gene encoding Planh was previously assigned to rat chromosome 12, which allowed us to assign the entire linkage group to this chromosome. These markers were highly polymorphic in 13 additional inbred rat strains (BUF/N, BN/SsN, WKY/N, MNR/N, LER/N, WBB1/N, WBB2/N, MR/N, LOU/MN, SHR/N, ACI/N, SR/Jr, and SS/Jr). These markers should be useful tools for further genetic studies in rats.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00553460
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  • 4
    Electronic Resource
    Electronic Resource
    Four polymorphic markers on rat chromosome 12 form a single linkage group (1993)
    Springer
    Biochemical genetics 31 (1993), S. 441-448 
    Details
    ISSN: 1573-4927
    Keywords: linkage analysis ; serine dehydratase ; plasminogen activator inhibitor ; simple sequence repeats ; microsatellites ; rat chromosome 12
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology
    Notes: Abstract Four PCR-typable polymorphic markers were mapped to rat chromosome 12 by linkage analysis of F2 intercross progeny of Fischer (F344/N) and Lewis (LEW/N) rat strains. The markers formed a single linkage group, covering 27.7 cM, with the following order and distance between markers: plasminogen activator inhibitor (Planh)—0.0 cM—phosphoenolpyruvate carboxykinase-related sequence 2 (Pepckr2)—15.4 cM—anonymous marker (D12N155)—12.3 cM—serine dehydratase (Sdh). All markers were identified and genotyped by PCR analysis of simple sequence repeats. The gene encoding Planh was previously assigned to rat chromosome 12, which allowed us to assign the entire linkage group to this chromosome. These markers were highly polymorphic in 13 additional inbred rat strains (BUF/N, BN/SsN, WKY/N, MNR/N, LER/N, WBB1/N, WBB2/N, MR/N, LOU/MN, SHR/N, ACI/N, SR/Jr, and SS/Jr). These markers should be useful tools for further genetic studies in rats.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02396228
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  • 5
    Electronic Resource
    Electronic Resource
    On Shortest k-Edge-Connected Steiner Networks in Metric Spaces (2000)
    Springer
    Journal of combinatorial optimization 4 (2000), S. 99-107 
    Details
    ISSN: 1573-2886
    Keywords: k-edge-connectivity ; spanning networks ; Steiner networks ; Steiner ratio
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Given a set of points P in a metric space, let l(P) denote the ratio of lengths between the shortest k-edge-connected Steiner network and the shortest k-edge-connected spanning network on P, and let r = inf l(P) ∣ P for k ≥ 1. In this paper, we show that in any metric space, r ≥ 3/4 for k ≥ 2, and there exists a polynomial-time α-approximation for the shortest k-edge-connected Steiner network, where α = 2 for even k and α = 2 + 4/(3k) for odd k. In the Euclidean plane, $$r_k \geqslant \sqrt 3 /2,\;\;r_3 \leqslant (\sqrt 3 + 2)/4$$ and $$r_4 \leqslant (7 + 3\sqrt 3 )/(9 + 2\sqrt 3 )$$ .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009889023408
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