Fully Dynamic All-Pairs Shortest Paths: Breaking the O(n) Barrier

A fully dynamic approximate distance oracle is a distance reporting data structure that supports dynamic insert edge and delete edge operations. In this paper we break a longstanding barrier in the design of fully dynamic all-pairs approximate distance oracles. All previous results for this model incurred an amortized cost of at least Omega(n) per operation. We present the first construction that provides constant stretch and o(m) amortized update time. For graphs that are not too dense (where |E| = O(|V|^{2-delta}) for some delta>0 we break the O(n) barrier and provide the first construction with constant stretch and o(n) amortized cost