Extend dependable spanner constructions beyond Euclidean spaces to doubling and general metric spaces

Extend the dependable (1+epsilon)-spanner construction developed for point sets in R^d under independent edge failures with survival probability p to doubling metrics and to general metric spaces, achieving analogous guarantees.

Background

All stated constructions and guarantees in the paper are for Euclidean spaces R^d, leveraging geometric tools such as LSOs to obtain near-linear-size spanners with few-hop paths that withstand random edge failures.

Generalizing these results to doubling or arbitrary metric spaces would broaden applicability but requires overcoming the lack of Euclidean geometric structure and potentially replacing LSOs with appropriate metric embeddings or structural decompositions.