The complexity of two graph orientation problems

Eggemann, N. and Noble, Steven (2012) The complexity of two graph orientation problems. Discrete Applied Mathematics 160 (4-5), pp. 513-517. ISSN 0166-218X.

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Official URL: https://doi.org/10.1016/j.dam.2011.10.036

Abstract

We consider two orientation problems in a graph, namely the minimization of the sum of all the shortest path lengths and the minimization of the diameter. Our main result is that for each positive integer , there is a linear-time algorithm that decides for a planar graph whether there is an orientation for which the diameter is at most . We also extend this result from planar graphs to any minor-closed family not containing all apex graphs. In contrast, it is known to be NP-complete to decide whether a graph has an orientation such that the sum of all the shortest path lengths is at most an integer specified in the input. We give a simpler proof of this result.

Metadata

Item Type:	Article
School:	Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
Depositing User:	Administrator
Date Deposited:	06 Jan 2023 14:22
Last Modified:	09 Aug 2023 12:54
URI:	https://eprints.bbk.ac.uk/id/eprint/50373

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