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• W2004598081 abstract "The routing problem in VLSI-layout can be modeled as a problem of packing node-disjoint Steiner trees in a graph. The problem is as follows: Given an undirected network G = (V, E) and a net list Ψ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mo>{</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mtext> </mml:mtext><mml:mi>i</mml:mi><mml:mtext> </mml:mtext><mml:mo>=</mml:mo><mml:mtext> </mml:mtext><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>...</mml:mn><mml:mo>,</mml:mo><mml:mtext> </mml:mtext><mml:mi>r</mml:mi><mml:mo>}</mml:mo></mml:mrow></mml:math> , a family <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msub><mml:mi>Γ</mml:mi><mml:mi>G</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>{</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mtext> </mml:mtext><mml:mo>=</mml:mo><mml:mtext> </mml:mtext><mml:mo stretchy=false>(</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mtext> </mml:mtext></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mtext> </mml:mtext><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo stretchy=false>)</mml:mo><mml:mo>,</mml:mo><mml:mtext> </mml:mtext><mml:mi>i</mml:mi><mml:mtext> </mml:mtext><mml:mo>=</mml:mo><mml:mtext> </mml:mtext><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>...</mml:mn><mml:mo>,</mml:mo><mml:mtext> </mml:mtext><mml:mi>r</mml:mi><mml:mo>}</mml:mo></mml:mrow></mml:math> is a node-disjoint family of Steiner trees spanning Ψ if <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math> , is a Steiner tree spanning <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math> for i = 1, ..., r and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mtext> </mml:mtext><mml:mo>∩</mml:mo><mml:mtext> </mml:mtext><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math> = for i ≠ j. The edge-disjoint version of this problem is known to be NP-hard for t. series-parallel graphs (see Rlchey and Parker [5]). In this paper we give a <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>O</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mn>5</mml:mn></mml:msup><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:math> algorithm for finding a minimum-cost node-disjoint family of Steiner trees in series-parallel networks. Our algorithm can be extended to k-trees and is polynomial for fixed k." @default.
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• W2004598081 title "Minimum-Cost Node-Disjoint Steiner Trees in Series-Parallel Networks" @default.
• W2004598081 doi "https://doi.org/10.1155/1996/43738" @default.
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