Planar Steiner Orientation is NP-complete

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2018
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Kryven, Myroslav
Löffler, Andre
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Many applications in graph theory are motivated by routing or flow problems. Among these problems is Steiner Orientation: given a mixed graph G (having directed and undirected edges) and a set T of k terminal pairs in G, is there an orientation of the undirected edges in G such that there is a directed path for every terminal pair in T ? This problem was shown to be NP -complete by Arkin and Hassin and later W [1]-hard by Pilipczuk and Wahlström, parametrized by k. On the other hand, there is an XP algorithm by Cygan et al. and a polynomial time algorithm for graphs without directed edges by Hassin and Megiddo. Chitnis and Feldmann showed W [1]-hardness of the problem for graphs of genus 1. We consider a further restriction to planar graphs and show NP -completeness.

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ISO 690BECK, Moritz, Johannes BLUM, Myroslav KRYVEN, Andre LÖFFLER, Johannes ZINK, 2018. Planar Steiner Orientation is NP-complete
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@unpublished{Beck2018-04-20T08:57:39ZPlana-44518,
  year={2018},
  title={Planar Steiner Orientation is NP-complete},
  author={Beck, Moritz and Blum, Johannes and Kryven, Myroslav and Löffler, Andre and Zink, Johannes}
}
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