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

Authors Zachary Friggstad, Ramin Mousavi

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Zachary Friggstad
  • Department of Computing Science, University of Alberta, Canada
Ramin Mousavi
  • Department of Computing Science, University of Alberta, Canada

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Zachary Friggstad and Ramin Mousavi. An O(log k)-Approximation for Directed Steiner Tree in Planar Graphs. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 63:1-63:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


We present an O(log k)-approximation for both the edge-weighted and node-weighted versions of Directed Steiner Tree in planar graphs where k is the number of terminals. We extend our approach to Multi-Rooted Directed Steiner Tree, in which we get a O(R+log k)-approximation for planar graphs for where R is the number of roots.

Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
  • Directed Steiner tree
  • Combinatorial optimization
  • approximation algorithms


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