Publikation:

Edge-Disjoint Paths in Planar Graphs with Short Total Length

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preprint_019.pdf
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Datum

1996

Autor:innen

Brandes, Ulrik
Neyer, Gabriele
Wagner, Dorothea

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Konstanzer Schriften in Mathematik und Informatik

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http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-20108
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Open Access Green

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Informatik und Informationswissenschaft: Publikationen
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Preprint
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Zusammenfassung

The problem of finding edge-disjoint paths in a planar graph such that each path connects two specified vertices on the outer face of the graph is well studied. The "classical" Eulerian case introduced by Okamura and Seymour is solvable in linear time by an Algorithm introduced by Wagner and Weihe. So far, the length of the paths were not considered. In this paper now, we prove that the problem of finding edge-disjoint paths of minimum total length in a planar graph is NP-hard, even if the graph fullfills the Eulerian condition and the maximum degree is four. Minimizing the length of the longest path is NP-hard as well. Efficient heuristics based on the algorithm by Wagner and Weihe are presented that determine edge-disjoint paths of small total length. We have implemented these heuristics and have studied their behaviour. It turns out that some of the heuristics are empirically very successful.

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004 Informatik

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ISO 690BRANDES, Ulrik, Gabriele NEYER, Dorothea WAGNER, 1996. Edge-Disjoint Paths in Planar Graphs with Short Total Length
BibTex
@unpublished{Brandes1996EdgeD-5975,
  year={1996},
  title={Edge-Disjoint Paths in Planar Graphs with Short Total Length},
  author={Brandes, Ulrik and Neyer, Gabriele and Wagner, Dorothea}
}
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    <dcterms:abstract xml:lang="eng">The problem of finding edge-disjoint paths in a planar graph such that each path connects two specified vertices on the outer face of the graph is well studied. The "classical" Eulerian case introduced by Okamura and Seymour is solvable in linear time by an Algorithm introduced by Wagner and Weihe. So far, the length of the paths were not considered. In this paper now, we prove that the problem of finding edge-disjoint paths of minimum total length in a planar graph is NP-hard, even if the graph fullfills the Eulerian condition and the maximum degree is four. Minimizing the length of the longest path is NP-hard as well. Efficient heuristics based on the algorithm by Wagner and Weihe are presented that determine edge-disjoint paths of small total length. We have implemented these heuristics and have studied their behaviour. It turns out that some of the heuristics are empirically very successful.</dcterms:abstract>
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