## Abstract

This research was supported in part by a Walter and Abstract. A k-spanner of a connected (undirected unweighted) graph G = (V, E) is a subgraph G' consisting of all the vertices of V and a subset of the edges, with the additional property that the distance between any two vertices in G' is larger than that distance in G by no more than a factor of k. This paper is concerned with approximating the problem of finding a 2-spanner in a given graph, with minimum maximum degree. We first show that the problem is at least as hard to approximate as set cover. Then a randomized approximation algorithm is provided for this problem, with approximation ratio of Õ(Δ^{1/4}). We then present a probabilistic algorithm that is more efficient for sparse graphs. Our algorithms are converted into deterministic ones using derandomization.

Original language | English |
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Pages (from-to) | 1438-1456 |

Number of pages | 19 |

Journal | SIAM Journal on Computing |

Volume | 27 |

Issue number | 5 |

DOIs | |

State | Published - 1998 |

## Keywords

- Approximation
- Graph spanners
- Np-hardness
- Randomized rounding