2026-07-20T05:23:43Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:2497 2024-03-06T11:09:05Z ddc:004 open_access

Approximating minimum cost connectivity problems Kortsarz, Guy Nutov, Zeev Connectivity laminar uncrossing Mader's Theorem power problems We survey approximation algorithms of connectivity problems. The survey presented describing various techniques. In the talk the following techniques and results are presented. 1)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] . We show how to use this to obtain a ratio 2 approximation for the min cost edge k-connectivity problem. 2)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. We also show results for the min power vertex k-connected problem using this lemma. We show that the min power is equivalent to the min-cost case with respect to approximation. 3)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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Guy Kortsarz and Zeev Nutov 2010 Is Part Of Dagstuhl Seminar Proceedings, Volume 9511, Parameterized complexity and approximation algorithms (2010) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.09511.4 urn:nbn:de:0030-drops-24975 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09511.4 eng https://creativecommons.org/licenses/by/4.0/legalcode