## Abstract

We consider the problem of finding a minimum edge cost subgraph of a graph satisfying both given node-connectivity requirements and degree upper bounds on nodes. We present an iterative rounding algorithm of the biset linear programming relaxation for this problem. For directed graphs and k-out-connectivity requirements from a root, our algorithm computes a solution that is a 2-approximation on the cost, and the degree of each node v in the solution is at most 2b(ρ) + O(k), where b(ρ) is the degree upper bound on v. For undirected graphs and elementconnectivity requirements with maximum connectivity requirement k, our algorithm computes a solution that is a 4-approximation on the cost, and the degree of each node v in the solution is at most 4b(ρ) + O(k). These ratios improve the previous O(log k)-approximation on the cost and O(2^{k}b(ρ))-approximation on the degrees. Our algorithms can be used to improve approximation ratios for other node-connectivity problems such as undirected k-out-connectivity, directed and undirected k-connectivity, and undirected rooted k-connectivity and subset k-connectivity.

Original language | English |
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Pages (from-to) | 1202-1229 |

Number of pages | 28 |

Journal | SIAM Journal on Computing |

Volume | 44 |

Issue number | 5 |

DOIs | |

State | Published - 2015 |

### Bibliographical note

Publisher Copyright:© 2015 Society for Industrial and Applied Mathematics.

## Keywords

- Approximation algorithm
- Iterative rounding
- Network design
- Node-connectivity