We give a dynamic programming solution to find the minimum cost of a diameter constrained Steiner tree in case of directed graphs. Then we show a simple reduction from undirected version to the directed version to realize an algorithm of similar complexity i.e, FPT in number of terminal vertices. Other natural variants of constrained Steiner trees are defined by imposing constraints on the min-degree and size of the Steiner tree and some polynomial time reductions among these problems are proven. To the best of our knowledge, these fairly simple reductions are not present in the literature prior to our work.
翻译:我们给出一个动态的编程解决方案,以找到直径受限的施泰纳树在有定向图表的情况下的最低成本。然后,我们从未定向版本向定向版本简单削减,以实现同样复杂的算法,即终端脊椎数的FPT。 施泰纳树受限的其他自然变体的定义是,对施泰纳树的微度和大小施加限制,以及这些问题中的某些多元时间缩短。 据我们所知,这些相当简单的缩减在我们工作之前的文献中并不存在。