Planar Steiner Orientation is NP-complete

Beck, Moritz; Blum, Johannes; Kryven, Myroslav; Löffler, Andre; Zink, Johannes

Planar Steiner Orientation is NP-complete

Files

Beck_2-b4bo2o1xb2qr0.pdf(134.53 KB)

Date

2018

Authors

Beck, Moritz

Blum, Johannes

Kryven, Myroslav

Löffler, Andre

Zink, Johannes

Publication type

Preprint

Publication status

Published

Abstract

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.

Subject (DDC)

004 Computer Science

Cite This

ISO 690

BECK, Moritz, Johannes BLUM, Myroslav KRYVEN, Andre LÖFFLER, Johannes ZINK, 2018. Planar Steiner Orientation is NP-complete

BibTex

@unpublished{Beck2018-04-20T08:57:39ZPlana-44518,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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Bibliography of Konstanz

Yes