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Computing the Shortest Network under a Fixed Topology
September 2002 (vol. 51 no. 9)
pp. 1117-1120

Abstract—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 $\big. \lambda\bigr.$ legal orientations for any fixed integer $\big. \lambda \ge 2\bigr.$. This settles an open problem posed in a recent paper [3].

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Index Terms:
Steiner trees, shortest network under a fixed topology, uniform orientation metric plane, linear programming.
Citation:
Guoliang Xue, K. Thulasiraman, "Computing the Shortest Network under a Fixed Topology," IEEE Transactions on Computers, vol. 51, no. 9, pp. 1117-1120, Sept. 2002, doi:10.1109/TC.2002.1032631
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