Abstract
Research on the full Steiner tree problem in the Euclidean plane R2 has important theoretic significance, and it also has broad applications in material construction, VLSI design, WDM optical networks and wireless communications. In this paper, combining with the material construction and the actual cost, we introduce two new variants of the full Steiner tree problem in the Euclidean plane R2: the minimumlength full Steiner tree problem (MLFST, for short) and the minimum-number of Steiner points in the full Steiner tree problem (MNPFST, for short). These problems are both NP-hard, and we design one approximation algorithm for each of them which have important applications in real life. To enhance the convenience of application, a subdivision procedure method and a minimum disk cover of points method are adopted in some designed algorithms.
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