### Abstract

Given a simple graph G = (V, E), the goal is to find a smallest set F of new edges such that G = (V, E union F) is k-edge-connected and simple. Very recently this problem was shown to be NP-hard by the second author. In this paper we prove that if OPT_{P}^{k} is high enough - depending on k only - then OPT_{S}^{k} = OPT_{P}^{k} holds, where OPT_{S}^{k} (OPT_{P}^{k}) is the size of an optimal solution of the augmentation problem with (without) the simplicity-preserving requirement, respectively. Furthermore, OPT_{S}^{k}-OPT_{P}^{k}≤g(k) holds for a certain (quadratic) function of k. Based on these results an algorithm is given which computes an optimal solution in time O(n^{4}) for any fixed k. Most of these results are extended to the case of non-uniform demands, as well.

Original language | English |
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Pages (from-to) | 486-495 |

Number of pages | 10 |

Journal | Annual Symposium on Foundations of Computer Science - Proceedings |

Publication status | Published - Dec 1 1997 |

Event | Proceedings of the 1997 38th IEEE Annual Symposium on Foundations of Computer Science - Miami Beach, FL, USA Duration: Oct 20 1997 → Oct 22 1997 |

### ASJC Scopus subject areas

- Hardware and Architecture

## Cite this

*Annual Symposium on Foundations of Computer Science - Proceedings*, 486-495.