When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2015.238
URN: urn:nbn:de:0030-drops-49170
URL: https://drops.dagstuhl.de/opus/volltexte/2015/4917/
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### Network Design Problems with Bounded Distances via Shallow-Light Steiner Trees

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### Abstract

In a directed graph G with non-correlated edge lengths and costs, the network design problem with bounded distances asks for a cost-minimal spanning subgraph subject to a length bound for all node pairs. We give a bi-criteria (2+\varepsilon,O(n^{0.5+\varepsilon}))-approximation for this problem. This improves on the currently best known linear approximation bound, at the cost of violating the distance bound by a factor of at most 2+\varepsilon.

In the course of proving this result, the related problem of directed shallow-light Steiner trees arises as a subproblem. In the context of directed graphs, approximations to this problem have been elusive. We present the first non-trivial result by proposing a (1+\varepsilon,O(|R|^{\varepsilon}))-ap\-proximation, where R is the set of terminals.

Finally, we show how to apply our results to obtain an (\alpha+\varepsilon,O(n^{0.5+\varepsilon}))-approximation for light-weight directed \alpha-spanners. For this, no non-trivial approximation algorithm has been known before. All running times depends on n and
\varepsilon and are polynomial in n for any fixed \varepsilon>0.

### BibTeX - Entry

@InProceedings{chimani_et_al:LIPIcs:2015:4917,
author =	{Markus Chimani and Joachim Spoerhase},
title =	{{Network Design Problems with Bounded Distances via Shallow-Light Steiner Trees}},
booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
pages =	{238--248},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-78-1},
ISSN =	{1868-8969},
year =	{2015},
volume =	{30},
editor =	{Ernst W. Mayr and Nicolas Ollinger},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},