New Doubling Spanners: Better and Simpler

Abstract

AbstractIn a seminal STOC’95 paper, Arya et al. conjectured that spanners for low-dimensional Euclidean spaces with constant maximum degree, hop-diameter O(logn) and lightness O(logn) (i.e., weight \(O(\log n) \cdot w(\textsf{MST}))\) can be constructed in O(n logn) time. This conjecture, which became a central open question in this area, was resolved in the affirmative by Elkin and Solomon in STOC’13 (even for doubling metrics).In this work we present a simpler construction of spanners for doubling metrics with the above guarantees. Moreover, our construction extends in a simple and natural way to provide k-fault tolerant spanners with maximum degree O(k 2), hop-diameter O(logn) and lightness O(k 2 logn).