TY - UNPB

T1 - Near-Optimal O(k)-Robust Geometric Spanners

AU - Bose, Prosenjit

AU - Carmi, Paz

AU - Dujmovic, Vida

AU - Morin, Pat

PY - 2018

Y1 - 2018

N2 - For any constants d ≥ 1, ǫ > 0, t > 1, and any n-point set P ⊂ R d , we show that there is a geometric graph G = (P,E) having O(nlog2 nlog logn) edges with the following property: For any F ⊆ P, there exists F + ⊇ F, |F + | ≤ (1 + ǫ)|F| such that, for any pair p, q ∈ P \ F + , the graph G − F contains a path from p to q whose (Euclidean) length is at most t times the Euclidean distance between p and q. In the terminology of robust spanners (Bose et al., SICOMP, 42(4):1720–1736, 2013) the graph G is a (1+ǫ)k-robust t-spanner of P. This construction is sparser than the recent constructions of Buchin, Olah, and Har- Peled ( ` arXiv:1811.06898) who prove the existence of (1 + ǫ)k-robust t-spanners with nlog O(d)n edges.

AB - For any constants d ≥ 1, ǫ > 0, t > 1, and any n-point set P ⊂ R d , we show that there is a geometric graph G = (P,E) having O(nlog2 nlog logn) edges with the following property: For any F ⊆ P, there exists F + ⊇ F, |F + | ≤ (1 + ǫ)|F| such that, for any pair p, q ∈ P \ F + , the graph G − F contains a path from p to q whose (Euclidean) length is at most t times the Euclidean distance between p and q. In the terminology of robust spanners (Bose et al., SICOMP, 42(4):1720–1736, 2013) the graph G is a (1+ǫ)k-robust t-spanner of P. This construction is sparser than the recent constructions of Buchin, Olah, and Har- Peled ( ` arXiv:1811.06898) who prove the existence of (1 + ǫ)k-robust t-spanners with nlog O(d)n edges.

M3 - Preprint

BT - Near-Optimal O(k)-Robust Geometric Spanners

ER -