Sparsification lower bound for linear spanners in directed graphs

For α≥1, β≥0, and a graph G, spanning subgraph H of G is said to be an (α,β)-spanner if dist(u,v,H)≤α⋅dist(u,v,G)+β holds for any pair vertices u v. These type spanners, called linear generalizes additive spanners multiplicative spanners. Recently, Fomin, Golovach, Lochet, Misra, Saurabh, Sharma initiated the study directed graphs (IPEC 2020). In this article, we continue line research prove that Directed Linear Spanner parameterized by number n admits no polynomial compression size O(n2−ϵ) ϵ>0 unless NP⊆coNP/poly. We show similar results hold Additive Multiplicative problems. This sparsification lower bound even when input acyclic α,β are computable functions distance being approximated.