Formally, for a positive integertand a graphG, a spanningsubgraphHofGis said to be amultiplicativet-spannerifdistH(u,v)≤t·distG(u,v)holdsfor any pair of verticesuandv.

or a positive integertand a graphG, aspanning subgraphHofGis said to be anadditivet-spannerifdistH(u,v)≤distG(u,v) +tholds for any pair of verticesuandv.

s a common generalization of these two concepts,(α,β)-spanners have also been studiedin the literature. Forα≥1,β≥0, and a graphG, a spanning subgraphHofGis said tobe an(α,β)-spannerifdistH(u,v)≤α·distG(u,v) +βholds for any pair of verticesuandv.