We give a simple algorithm for maintaining a n^{o(1)}-approximate spanner H of a graph G with n vertices as G receives edge updates by reduction to the dynamic All-Pairs Shortest Paths (APSP) problem. Given an initially empty graph G, our algorithm processes m insertions and n deletions in total time m^{1 + o(1)} and maintains an initially empty spanner H with total recourse n^{1 + o(1)}. When the number of insertions is much larger than the number of deletions, this notably yields recourse sub-linear in the total number of updates.
Our simple algorithm can be extended to maintain a δ ≥ ω(1)-approximate spanner with n^{1+o(1)} edges throughout a sequence of m insertions and D deletions with amortized update time n^{o(1)} and total recourse n^{1 + o(1)} + n^{o(1)} ⋅ D via batching
