Type of Publication:  Preprint 
URI (citable link):  http://nbnresolving.de/urn:nbn:de:bsz:352opus20108 
Author:  Brandes, Ulrik; Neyer, Gabriele; Wagner, Dorothea 
Year of publication:  1996 
Series:  Konstanzer Schriften in Mathematik und Informatik ; 19 
Summary: 
The problem of finding edgedisjoint 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 edgedisjoint paths of minimum total length in a planar graph is NPhard, even if the graph fullfills the Eulerian condition and the maximum degree is four. Minimizing the length of the longest path is NPhard as well. Efficient heuristics based on the algorithm by Wagner and Weihe are presented that determine edgedisjoint 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.

Subject (DDC):  004 Computer Science 
Link to License:  In Copyright 
BRANDES, Ulrik, Gabriele NEYER, Dorothea WAGNER, 1996. EdgeDisjoint Paths in Planar Graphs with Short Total Length
@unpublished{Brandes1996EdgeD5975, title={EdgeDisjoint Paths in Planar Graphs with Short Total Length}, year={1996}, author={Brandes, Ulrik and Neyer, Gabriele and Wagner, Dorothea} }
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