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<p><b>Abstract</b>—We show that, in any given uniform orientation metric plane, the shortest network interconnecting a given set of points under a fixed topology can be computed by solving a linear programming problem whose size is bounded by a polynomial in the number of terminals and the number of legal orientations. When the given topology is restricted to a Steiner topology, our result implies that the Steiner minimum tree under a given Steiner topology can be computed in polynomial time in any given uniform orientation metric with <tmath>$\big. \lambda\bigr.$</tmath> legal orientations for any fixed integer <tmath>$\big. \lambda \ge 2\bigr.$</tmath>. This settles an open problem posed in a recent paper [<ref rid="bibT11173" type="bib">3</ref>].</p>
Steiner trees, shortest network under a fixed topology, uniform orientation metric plane, linear programming.
Guoliang Xue, K. Thulasiraman, "Computing the Shortest Network under a Fixed Topology", IEEE Transactions on Computers, vol. 51, no. , pp. 1117-1120, September 2002, doi:10.1109/TC.2002.1032631
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