Issue No. 09 - September (2002 vol. 51)
<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.
G. Xue and K. Thulasiraman, "Computing the Shortest Network under a Fixed Topology," in IEEE Transactions on Computers, vol. 51, no. , pp. 1117-1120, 2002.