Graph Orientation and Flows over Time

Arulselvan, Ashwin; Groß, Martin; Skutella, Martin

doi:10.1007/978-3-319-13075-0_58

“…Graph orientation and network flows Graph orientation is connected to network flow theory both from a structural point of view as well as in the context of applications, e.g., in evacuation planning (Wolshon 2001) and traffic management (Hausknecht et al 2011), where certain arcs of the network may be reversed in order to enable faster evacuation or to resolve traffic jams; see also the recent complexity results by Rebennack et al (2010) and Arulselvan et al (2014). In the next section, we will make use of the well-known fact that the fixed-degree orientation problem is equivalent to the maximum flow problem with unit capacities.…”

Section: Degree-constrained Orientationsmentioning

confidence: 99%

Degree-constrained orientations of embedded graphs

Disser

¹

,

Matuschke

²

2014

J Comb Optim

7

0

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We investigate the problem of orienting the edges of an embedded graph in such a way that the resulting digraph fulfills given in-degree specifications both for the vertices and for the faces of the embedding. This primal-dual orientation problem was first proposed by Frank for the case of planar graphs, in conjunction with the question for a good characterization of the existence of such orientations. We answer this question by showing that a feasible orientation of a planar embedding, if it exists, can be constructed by combining certain parts of a primally feasible orientation and a dually feasible orientation. For the general case of arbitrary embeddings, we show that the number of feasible orientations is bounded by 2 2g , where g is the genus of the embedding. Our proof also yields a fixed-parameter algorithm for determining all feasible orientations parameterized by the genus. In contrast to these positive results, however, we also show that the problem becomes NP-complete even for a fixed genus if only upper and lower bounds on the in-degrees are specified instead of exact values.

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“…Graph orientation and network flows. Graph orientation is connected to network flow theory both from a structural point of view as well as in the context of applications, e.g., in evacuation planning (Wolshon, 2001) and traffic management (Hausknecht et al, 2011), where certain arcs of the network may be reversed in order to enable faster evacuation or to resolve traffic jams; see also the recent complexity results by Rebennack et al (2010) and Arulselvan et al (2013). In the next section, we will make use of the fact that the fixeddegree orientation problem is equivalent to the maximum flow problem with unit capacities.…”

Section: Related Workmentioning

confidence: 99%

Degree-Constrained Orientations of Embedded Graphs

Disser

¹

,

Matuschke

²

2012

Algorithms and Computation

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We investigate the problem of orienting the edges of an embedded graph in such a way that the resulting digraph fulfills given in-degree specifications both for the vertices and for the faces of the embedding. This primal-dual orientation problem was first proposed by Frank for the case of planar graphs, in conjunction with the question for a good characterization of the existence of such orientations. We answer this question by showing that a feasible orientation of a planar embedding, if it exists, can be constructed by combining certain parts of a primally feasible orientation and a dually feasible orientation. For the general case of arbitrary embeddings, we show that the number of feasible orientations is bounded by 2 2g , where g is the genus of the embedding. Our proof also yields a fixed-parameter algorithm for determining all feasible orientations parameterized by the genus. In contrast to these positive results, however, we also show that the problem becomes NP-complete even for a fixed genus if only upper and lower bounds on the in-degrees are specified instead of exact values.

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“…An extended abstract has appeared in proceedings of the 25th International Symposium on Algorithms and Computation (ISAAC '14).…”

mentioning

confidence: 99%

Graph orientation and flows over time

Arulselvan

¹

,

Groβ

²

,

Skutella

³

2015

Networks

Self Cite

1

0

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Flows over time are used to model many real-world logistic and routing problems. The networks underlying such problems - streets, tracks, etc. - are inherently undirected and directions are only imposed on them to reduce the danger of colliding vehicles and similar problems. Thus, the question arises, what influence the orientation of the network has on the network flow over time problem that is being solved on the oriented network. In the literature, this is also referred to as the contraflow or lane reversal problem. We introduce and analyze the price of orientation: How much flow is lost in any orientation of the network if the time horizon remains fixed? We prove that there is always an orientation where we can still send one-third of the flow and this bound is tight. For the special case of networks with a single source or sink, this fraction is half, which is again tight. We present more results of similar flavor and also show nonapproximability results for finding the best orientation for single and multicommodity maximum flows over time

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Graph Orientation and Flows over Time

Cited by 3 publications

References 19 publications

Degree-constrained orientations of embedded graphs

Degree-constrained orientations of embedded graphs

Degree-Constrained Orientations of Embedded Graphs

Graph orientation and flows over time

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