{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article2644","name":"Approximating minimum cost connectivity problems","abstract":"We survey approximation algorithms of connectivity problems.\r\nThe survey presented describing various techniques. In the talk the following techniques and results are presented. \r\n\r\n1)Outconnectivity: Its well known that there exists a polynomial time algorithm to solve the problems of finding an edge k-outconnected from r subgraph [EDMONDS] and a vertex k-outconnectivity subgraph from r [Frank-Tardos] . \r\nWe show how to use this to obtain a ratio 2 approximation for the min cost edge k-connectivity \r\nproblem. \r\n\r\n2)The critical cycle theorem of Mader: We state a fundamental theorem of Mader and use it to provide a 1+(k-1)\/n ratio approximation for the min cost vertex k-connected subgraph, in the metric case.\r\nWe also show results for the min power vertex k-connected problem using this lemma.\r\nWe show that the min power is equivalent to the min-cost case with respect to approximation.\r\n\r\n3)Laminarity and uncrossing: We use the well known laminarity of a BFS solution and show a simple new proof due to Ravi et al for Jain's 2 approximation for Steiner network.","keywords":["Connectivity","laminar","uncrossing","Mader's Theorem","power problems"],"author":[{"@type":"Person","name":"Kortsarz, Guy","givenName":"Guy","familyName":"Kortsarz"},{"@type":"Person","name":"Nutov, Zeev","givenName":"Zeev","familyName":"Nutov"}],"position":4,"pageStart":1,"pageEnd":0,"dateCreated":"2010-03-02","datePublished":"2010-03-02","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Kortsarz, Guy","givenName":"Guy","familyName":"Kortsarz"},{"@type":"Person","name":"Nutov, Zeev","givenName":"Zeev","familyName":"Nutov"}],"copyrightYear":"2010","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.09511.4","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume784","volumeNumber":9511,"name":"Dagstuhl Seminar Proceedings, Volume 9511","dateCreated":"2010-03-02","datePublished":"2010-03-02","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article2644","isPartOf":{"@type":"Periodical","@id":"#series119","name":"Dagstuhl Seminar Proceedings","issn":"1862-4405","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume784"}}}