An O(log k)-Approximation for Directed Steiner Tree in Planar Graphs

02/09/2023

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by   Zachary Friggstad, et al.

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We present an O(log k)-approximation for both the edge-weighted and node-weighted versions of in planar graphs where k is the number of terminals. We extend our approach to (in general graphs and 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.