New bicriteria approximation algorithms give polylog cost and O(log k) length slack for length-constrained Directed Steiner Tree and Forest on planar digraphs.
A polylogarithmic approximation for Directed Steiner Forest in planar digraphs
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Length-Constrained Network Design in Planar Digraphs
New bicriteria approximation algorithms give polylog cost and O(log k) length slack for length-constrained Directed Steiner Tree and Forest on planar digraphs.