MPI-INF/SWS Research Reports 1991-2021

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Approximating minimum size 1,2-connected networks

Krysta, Piotr

January 2001, 22 pages.

Status: available - back from printing

The problem of finding the minimum size 2-connected subgraph is a classical problem in network design. It is known to be NP-hard even on cubic planar graphs and Max-SNP hard. We study the generalization of this problem, where requirements of 1 or 2 edge or vertex disjoint paths are specified between every pair of vertices, and the aim is to find a minimum subgraph satisfying these requirements. For both problems we give $3/2$-approximation algorithms. This improves on the straightforward $2$-approximation algorithms for these problems, and generalizes earlier results for 2-connectivity. We also give analyses of the classical local optimization heuristics for these two network design problems.

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  AUTHOR = {Krysta, Piotr},
  TITLE = {Approximating minimum size {1,2}-connected networks},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-2001-1-001},
  MONTH = {January},
  YEAR = {2001},
  ISSN = {0946-011X},