eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2010-03-02
1
0
10.4230/DagSemProc.09511.4
article
Approximating minimum cost connectivity problems
Kortsarz, Guy
Nutov, Zeev
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09511/DagSemProc.09511.4/DagSemProc.09511.4.pdf
Connectivity
laminar
uncrossing
Mader's Theorem
power problems