{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article7721","name":"Network Design Problems with Bounded Distances via Shallow-Light Steiner Trees","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.\r\n \r\nIn 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.\r\n \r\nFinally, 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\r\n\\varepsilon and are polynomial in n for any fixed \\varepsilon>0.","keywords":["network design","approximation algorithm","shallow-light spanning trees","spanners"],"author":[{"@type":"Person","name":"Chimani, Markus","givenName":"Markus","familyName":"Chimani"},{"@type":"Person","name":"Spoerhase, Joachim","givenName":"Joachim","familyName":"Spoerhase"}],"position":22,"pageStart":238,"pageEnd":248,"dateCreated":"2015-02-26","datePublished":"2015-02-26","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Chimani, Markus","givenName":"Markus","familyName":"Chimani"},{"@type":"Person","name":"Spoerhase, Joachim","givenName":"Joachim","familyName":"Spoerhase"}],"copyrightYear":"2015","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.STACS.2015.238","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6233","volumeNumber":30,"name":"32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)","dateCreated":"2015-02-26","datePublished":"2015-02-26","editor":[{"@type":"Person","name":"Mayr, Ernst W.","givenName":"Ernst W.","familyName":"Mayr"},{"@type":"Person","name":"Ollinger, Nicolas","givenName":"Nicolas","familyName":"Ollinger"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article7721","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6233"}}}