Optimal Euclidean spanners: Really short, thin, and lanky Academic Article uri icon


  • Abstract The degree, the (hop-) diameter, and the weight are the most basic and well- studied parameters of geometric spanners. In a seminal STOC'95 paper, titled “Euclidean spanners: short, thin and lanky”, Arya et al.[1995] devised a construction of Euclidean (1+ ε)- spanners that achieves constant degree, diameter O (log n), weight O (log 2 n) ċ ω (MST), and has running time O (n ċ log n). This construction applies to n-point constant- dimensional Euclidean spaces. Moreover, Arya et al. conjectured that the weight bound can be improved by a logarithmic factor, without increasing the degree and the diameter of the spanner, and within the same running time. This conjecture of Arya et al. became one of the most central open problems in the area of Euclidean spanners. Nevertheless, the only progress since 1995 towards its resolution was achieved in the lower bounds front: Any …

publication date

  • November 2, 2015