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New (α,β) Spanners and Hopsets
[article]

2020
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arXiv
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pre-print

An f(d)-spanner of an unweighted n-vertex graph G=(V,E) is a subgraph H satisfying that dist_H(u, v) is at most f(dist_G(u, v)) for every u,v ∈ V. We present new spanner constructions that achieve a nearly optimal stretch of O( k /d ) for any distance value d ∈ [1,k^1-o(1)], and d ≥ k^1+o(1). We show the following: 1. There exists an f(d)-spanner H ⊆ G with f(d)≤ 7k for any d ∈ [1,√(k)/2] with expected size O_k(n^1+1/k). This in particular gives (α,β) spanners with α=O(√(k)) and β=O(k). 2. For

arXiv:1907.11402v2
fatcat:3eofx2y2qzagpmfye6rgqbguve