Deterministic Incremental APSP with Polylogarithmic Update Time and Stretch
share
We provide the first deterministic data structure that given a weighted undirected graph undergoing edge insertions, processes each update with polylogarithmic amortized update time and answers queries for the distance between any pair of vertices in the current graph with a polylogarithmic approximation in O(loglog n) time. Prior to this work, no data structure was known for partially dynamic graphs, i.e., graphs undergoing either edge insertions or deletions, with less than n^o(1) update time except for dense graphs, even when allowing randomization against oblivious adversaries or considering only single-source distances.
READ FULL TEXT