## Abstract

An (α,β)-spanner of a graph G is a subgraph H such that dist _{H} ≤ α · distt _{G}(u, ω) + β for every pair of vertices u, ω, where dist _{G′} (u, ω) denotes the distance between two vertices u and v in G′. It is known that every graph G has a polynomially constructible (2κ -1,0)-spanner (also known as multiplicative (2κ - 1)-spanner) of size O(n ^{1-1/κ}) for every integer κ ≥ 1, and a polynomially constructible (1, 2)-spanner (also known as additive 2-spanner) of size Ō(n ^{3/2}). This paper explores hybrid spanner constructions (involving both multiplicative and additive factors) for general graphs and shows that the multiplicative factor can be made arbitrarily close to 1 while keeping the spanner size arbitrarily close to O(n), at the cost of allowing the additive term to be a sufficiently large constant, More formally, we show that for any constant ∈,λ > 0 there exists a constant β= β(ε, λ) such that for every n-vertex graph G there is an efficiently constructible (1 + ε, β)-spanner of size O(n ^{1+λ}).

Original language | English |
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Pages (from-to) | 608-631 |

Number of pages | 24 |

Journal | SIAM Journal on Computing |

Volume | 33 |

Issue number | 3 |

DOIs | |

State | Published - 28 Jul 2004 |

Externally published | Yes |

## Keywords

- Graph algorithms
- Graph partitions
- Spanners