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Computing the shortest network under a fixed topology

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2 Author(s)
Guoliang Xue ; Dept. of Comput. Sci. & Eng., Arizona State Univ., Tempe, AZ, USA ; Thulasiraman, K.

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 λ legal orientations for any fixed integer λ ≥ 2. This settles an open problem posed by Brazil, Thomas and Weng (2000).

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Computers, IEEE Transactions on  (Volume:51 ,  Issue: 9 )