
OneWay Trail Orientations
Given a graph, does there exist an orientation of the edges such that th...
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Inapproximability within W[1]: the case of Steiner Orientation
In the kSteiner Orientation problem we are given a mixed graph, that is...
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The SingleFace Ideal Orientation Problem in Planar Graphs
We consider the ideal orientation problem in planar graphs. In this prob...
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The Complexity of Transitively Orienting Temporal Graphs
In a temporal network with discrete timelabels on its edges, entities a...
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Roundtrip Spanners with (2k1) Stretch
A roundtrip spanner of a directed graph G is a subgraph of G preserving ...
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Target Location Problem for Multicommodity Flow
Motivated by scheduling in Geodistributed data analysis, we propose a t...
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Maxflow vitality in undirected unweighted planar graphs
We show a fast algorithm for determining the set of relevant edges in a ...
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Planar Steiner Orientation is NPcomplete
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 [1] and later W [1]hard by Pilipczuk and Wahlström [7], parametrized by k. On the other hand, there is an XP algorithm by Cygan et al. [3] and a polynomial time algorithm for graphs without directed edges by Hassin and Megiddo [5]. Chitnis and Feldmann [2] 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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