We show how to construct (1+ε)-spanner over a set P of n
points in Rd that is resilient to a catastrophic failure of nodes.
Specifically, for prescribed parameters ϑ,ε∈(0,1), the
computed spanner G has O(ε−cϑ−6nlogn(loglogn)6) edges, where c=O(d). Furthermore, for any k, and
any deleted set B⊆P of k points, the residual graph G∖B is (1+ε)-spanner for all the points of P except for
(1+ϑ)k of them. No previous constructions, beyond the trivial clique
with O(n2) edges, were known such that only a tiny additional fraction
(i.e., ϑ) lose their distance preserving connectivity.
Our construction works by first solving the exact problem in one dimension,
and then showing a surprisingly simple and elegant construction in higher
dimensions, that uses the one-dimensional construction in a black box fashion