We present an $O(\log k)$-approximation for both the edge-weighted and node-weighted versions of \DST in planar graphs where $k$ is the number of terminals. We extend our approach to \MDST (in general graphs \MDST and \DST are easily seen to be equivalent but in planar graphs this is not the case necessarily) in which we get a $O(R+\log k)$-approximation for planar graphs for where $R$ is the number of roots.

翻译：在平面图中,以K美元为终端数的边加权和节加权两种版本的\DST, 我们提出了一个$O(\log k) 和$+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++