Approximating minimum size 1,2-connected networks

Krysta, Piotr

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Approximating minimum size 1,2-connected networks

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Krysta, Piotr
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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2001-1-001
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Krysta, P.(2001). Approximating minimum size 1,2-connected networks (MPI-I-2001-1-001). Saarbrücken: Max-Planck-Institut für Informatik.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-6D47-0

Abstract

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.