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Comment on "Computing the Shortest Network under a Fixed Topology'
June 2006 (vol. 55 no. 6)
pp. 783-784
In a recent paper [2], a linear programming formulation was given for the problem of computing a shortest network under a fixed topology (under the \lambda{\hbox{-}}{\rm metric}). We point out a nontrivial error in this paper and give a correct and simpler linear programming formulation. We also show that the result can be generalized to any distance function given by a Minkowski unit circle that is a centrally symmetric polygon.

[1] P. Widmayer, Y.F. Wu, and C.K. Wong, “On Some Distance Problems in Fixed Orientations,” SIAM J. Computing, vol. 16, no. 4, pp. 728-746, 1987.
[2] G. Xue and K. Thulasiraman, “Computing the Shortest Network under a Fixed Topology,” IEEE Trans. Computers, vol. 51, pp. 1117-1120, 2002.

Index Terms:
Steiner trees, shortest network under a fixed topology, polygonal Minkowski unit circle, linear programming.
Citation:
M. Zachariasen, "Comment on "Computing the Shortest Network under a Fixed Topology'," IEEE Transactions on Computers, vol. 55, no. 6, pp. 783-784, June 2006, doi:10.1109/TC.2006.84
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