Publication 2002 Issue No. 9 - September Abstract - Computing the Shortest Network under a Fixed Topology
Computing the Shortest Network under a Fixed Topology
September 2002 (vol. 51 no. 9)
pp. 1117-1120
 ASCII Text x Guoliang Xue, K. Thulasiraman, "Computing the Shortest Network under a Fixed Topology," IEEE Transactions on Computers, vol. 51, no. 9, pp. 1117-1120, September, 2002.
 BibTex x @article{ 10.1109/TC.2002.1032631,author = {Guoliang Xue and K. Thulasiraman},title = {Computing the Shortest Network under a Fixed Topology},journal ={IEEE Transactions on Computers},volume = {51},number = {9},issn = {0018-9340},year = {2002},pages = {1117-1120},doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2002.1032631},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Computing the Shortest Network under a Fixed TopologyIS - 9SN - 0018-9340SP1117EP1120EPD - 1117-1120A1 - Guoliang Xue, A1 - K. Thulasiraman, PY - 2002KW - Steiner treesKW - shortest network under a fixed topologyKW - uniform orientation metric planeKW - linear programming.VL - 51JA - IEEE Transactions on ComputersER -

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